1.
図書
Michael V. Sadovskii
2.
図書
M.S. Ramkarthik, Payal D. Solanki
出版情報:
Boca Raton : CRC Press, 2022 xxiii, 399 p. ; 27 cm
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3.
図書
with contributions by K. Binder ... [et al.] ; edited by K. Binder
4.
図書
F. Mandl
目次情報:
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The First Law of Thermodynamics
The Second Law of Thermodynamics
Paramagnetism
The Second Law of Thermodynamics II
Simple Thermodynamic Systems
The Heat Capacity of Solids
The Perfect Classical Gas
Phase Equilibria
The Prefect Quantal Gas
Black-Body Radiation
Systems With Variable Particle Numbers
The First Law of Thermodynamics
The Second Law of Thermodynamics
Paramagnetism
5.
図書
Piotr Garbaczewski
出版情報:
Singapore ; Philadelphia : World Scientific, c1985 xiii, 244 p. ; 23 cm
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6.
図書
James Glimm, Arthur Jaffe
出版情報:
New York ; Tokyo : Springer-Verlag, c1987 xxii, 535 p. ; 24 cm
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7.
図書
edited by K. Binder ; with contributions by K.Binder ... [et al.]
8.
図書
editor, H.J. Raveché
9.
図書
R.A. Minlos
10.
図書
Jean-François Sadoc and Rémy Mosseri
目次情報:
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Preface
Introduction to geometrical frustration / 1：
Ideal models / 2：
Finite structures / 3：
Decurving and disclinations / 4：
Hierarchical polytopes / 5：
Some physical properties / 6：
Periodic structures with large cells / 7：
Quasiperiodic order and frustration / 8：
Appendices
Bibliography
Index
Preface
Introduction to geometrical frustration / 1：
Ideal models / 2：
11.
図書
edited by Massimo Picardello, Wolfgang Woess
12.
図書
David P. Landau, Kurt Binder
出版情報:
Cambridge : Cambridge University Press, 2000 xiii, 384 p. ; 25 cm
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Preface
Introduction / 1：
Some necessary background / 2：
Simple sampling Monte Carlo methods / 3：
The metropolis Monte Carlo algorithm for lattice models / 4：
More on importance sampling Monte Carlo methods for lattice systems / 5：
Off-lattice models / 6：
Reweighting methods / 7：
Quantum Monte Carlo methods / 8：
Monte Carlo renormalization group methods / 9：
Non-equilibrium and irreversible processes / 10：
Lattice gauge models: a brief introduction / 11：
A brief review of other methods of computer simulation / 12：
Outlook / 13：
Preface
Introduction / 1：
Some necessary background / 2：
13.
図書
Walter E. Thirring ; with foreword by Elliott H. Lieb
出版情報:
Providence, R.I. : American Mathematical Society, c1998 xiii, 729 p. ; 26 cm
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14.
図書
edited by George H. Weiss
出版情報:
Philadelphia : Society for Industrial and Applied Mathematics, 1994 xviii, 253 p. ; 26 cm
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Diffusion kinetics in microscopic nonhomogeneous systems / Peter Clifford ; Nicholas J. B. Green
Fluctuations in nonlinear systems driven by colored noise / Mark Dykman ; Katja Lindenberg
Percolation / Shlomo Havlin ; Armin Bunde
Aspects of trapping in transport processes / Frank den Hollander ; George H. Weiss
Stochastic resonance: from the Ice Ages to the Monkey's / Ear Frank Moss
Diffusion kinetics in microscopic nonhomogeneous systems / Peter Clifford ; Nicholas J. B. Green
Fluctuations in nonlinear systems driven by colored noise / Mark Dykman ; Katja Lindenberg
Percolation / Shlomo Havlin ; Armin Bunde
15.
図書
V.A. Malyshev, R.A. Minlos
目次情報:
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Introduction
Extended introduction
Construction of a nonequilibrium dynamics
Construction of an equilibrium dynamics
Spectral analysis of the Euclidean field transfer matrix
Asymptotic completeness for interacting fermion systems
The method of Bethe-Salpeter kernels (Dyson's equation)
Guide to the Literature
References
Introduction
Extended introduction
Construction of a nonequilibrium dynamics
16.
図書
by E.M. Lifshitz and L.P. Pitaevskiĭ ; translated from the Russian by J.B. Sykes and M.J. Kearsley
目次情報:
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Fundamental principles of theoretical physics
The Gibbs distribution
Ideal gases
Solids
Non-ideal gases
Solutions
Chemical reactions
Fluctuations
Surfaces
Fundamental principles of theoretical physics
The Gibbs distribution
Ideal gases
17.
図書
by Y.M. Berezansky and Y.G. Kondratiev
18.
図書
Hagen Kleinert
出版情報:
Singapore : World Scientific, c1995 xxvii, 891 p. ; 23 cm
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19.
図書
20.
図書
by L.E. Reichl ; foreword by Ilya Prigogine ; [illustration by Pamela Vesterby]
出版情報:
Austin : University of Texas Press, c1980 xii, 709 p. ; 24 cm
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Thermodynamics
Introduction to Thermodynamics
The Thermodynamics of Phase Transitions
Concepts from Probability Theory
Elementary Probability Theory and Limit Theorems
Stochastic Dynamics and Brownian Motion
The Foundations of Statistical Mechanics
Equilibrium Statistical Mechanics
Order-Disorder Transitions and Renormalization Theory
Interacting Fluids
Nonequilibrium Statistical Mechanics
Hydrodynamic Processes Near Equilibrium
Transport Theory
Nonequilibrium Phase Transitions
Appendices
Indexes
Thermodynamics
Introduction to Thermodynamics
The Thermodynamics of Phase Transitions
21.
図書
R. Kubo, M. Toda, N. Hashitsume
22.
図書
Ilya Prigogine, Robert Herman
出版情報:
New York : American Elsevier, 1971 xix, 100 p. ; 22 cm
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23.
図書
[by] B. Jancovici. Problems by Yves Archambault. translated from the French by L. J. Carroll
出版情報:
London ; New York : McGraw-Hill, c1973 xi, 147 p. ; 23 cm
シリーズ名:
European physics series
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24.
図書
edited by K. Binder ; with contributions by A. Baumgärtner ... [et al.]
25.
図書
edited by Eric Goles and Servet Martínez
26.
図書
Roger Balian ; translated by D. ter Haar and J.F. Gregg
27.
図書
Boris Nahapetian
28.
図書
Rick Durrett, Harry Kesten, editors
29.
図書
Charles Ruhla ; translated from the French (La physique du hasard : de Blaise Pascal à Niels Bohr) by G. Barton
出版情報:
Oxford ; Tokyo : Oxford University Press, 1992 xi, 222 p. ; 24 cm
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The children of Democritus (prediction in science)
The laws of chaos (the theory of probability)
Gaussian deviations (the theory of physical measurements)
Maxwell, or probabilities as a matter of ignorance
Boltzmann, or probabilities as a matter of conviction (statistical physics)
Poincare, or deterministic chaos (sensitivity to initial conditions)
Bohr, or chance unavoidable (quantum mechanics)
Inseparable photons (the EPR paradox)
Conclusions (how chance does yeoman's service)
Bibliography
Index
The children of Democritus (prediction in science)
The laws of chaos (the theory of probability)
Gaussian deviations (the theory of physical measurements)
30.
図書
Neal Madras, Gordon Slade
31.
図書
[by] Don C. Kelly
出版情報:
New York : Academic Press, [1973] xiii, 421 p. ; 24 cm
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32.
図書
M. Toda, R. Kubo, N. Saitô
33.
図書
[by] B.R. Martin
出版情報:
London ; New York : Academic Press, 1971 xiii, 209 p. ; 24 cm
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34.
図書
edited by Zlatko Tesanovic
出版情報:
Redwood City, Calif. : Addison-Wesley Pub. Co., Advanced Book Program, c1990 viii, 208 p. ; 24 cm
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35.
図書
A. Ranfagni ... [et al]
36.
図書
by N.N. Bogolyubov, Jr. ; Translated and edited by P.J. Shepherd
37.
図書
Hagen Kleinert
出版情報:
Singapore ; Teaneck, N.J. : World Scientific, c1990 xxi, 664 p. ; 23 cm
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38.
図書
M. Toda, R. Kubo, N. Saitō
39.
図書
C. Kittel
出版情報:
New York : Wiley, c1958 , London : Chapman & Hall ix, 228 p. ; 24 cm
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40.
図書
by L. D. Landau and E. M. Lifshitz ; translated from the Russian by E. Peierls and R. F. Peierls
41.
図書
Gregory H. Wannier
出版情報:
New York : Dover Publications, 1987, c1966 xii, 532 p. ; 22 cm
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42.
図書
S. Ichimaru
出版情報:
Reading, Mass. ; Tokyo : W.A. Benjamin, 1973 xviii, 324 p. ; 24 cm
シリーズ名:
Frontiers in physics
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43.
図書
by Stephen G. Brush
出版情報:
Princeton, N.J. : Princeton University Press, c1983 ix, 356 p. ; 25 cm
シリーズ名:
Princeton series in physics
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44.
図書
D.J.A. Welsh
目次情報:
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The complexity of enumeration / 1：
Basics of complexity / 1.1：
Counting problems / 1.2：
# P-complete problems / 1.3：
Decision easy, counting hard / 1.4：
The Permanent / 1.5：
Hard enumeration problems not thought to be #P-complete / 1.6：
Self-avoiding walks / 1.7：
Toda's theorems / 1.8：
Additional notes / 1.9：
Knots and links / 2：
Introduction / 2.1：
Tait colourings / 2.2：
Classifying knots / 2.3：
Braids and the braid group / 2.4：
The braid index and the Seifert graph of a link / 2.5：
Enzyme action / 2.6：
The number of knots and links / 2.7：
The topology of polymers / 2.8：
Colourings, flows and polynomials / 2.9：
The chromatic polynomial / 3.1：
The Whitney-Tutte polynomials / 3.2：
Tutte Grothendieck invariants / 3.3：
Reliability theory / 3.4：
Flows over an Abelian group / 3.5：
Ice models / 3.6：
A catalogue of invariants / 3.7：
Statistical physics / 3.8：
Percolation processes / 4.1：
The Ising model / 4.2：
Combinatorial interpretations / 4.3：
The Ashkin-Teller-Potts model / 4.4：
The random cluster model / 4.5：
Percolation in the random cluster model / 4.6：
Link polynomials and the Tait conjectures / 4.7：
The Alexander polynomial / 5.1：
The Jones polynomial and Kauffman bracket / 5.2：
The Homfly polynomial / 5.3：
The Kauffman 2-variable polynomial / 5.4：
The Tait conjectures / 5.5：
Thistlethwaite's nontriviality criterion / 5.6：
Link invariants and statistical mechanics / 5.7：
Complexity questions / 5.8：
Computations in knot theory / 6.1：
The complexity of the Tutte plane / 6.2：
The complexity of knot polynomials / 6.3：
The complexity of the Ising model / 6.4：
Reliability and other computations / 6.5：
The complexity of uniqueness and parity / 6.6：
Unique solutions / 7.1：
Unambiguous machines and one-way functions / 7.2：
The Valiant-Vazirani theorem / 7.3：
Hard counting problems not parsimonious with SAT / 7.4：
The curiosity of parity / 7.5：
Toda's theorem on parity / 7.6：
Approximation and randomisation / 7.7：
Metropolis methods / 8.1：
Approximating to within a ratio / 8.2：
Generating solutions at random / 8.3：
Rapidly mixing Markov chains / 8.4：
Computing the volume of a convex body / 8.5：
Approximations and the Ising model / 8.6：
Some open questions / 8.7：
References / 8.8：
The complexity of enumeration / 1：
Basics of complexity / 1.1：
Counting problems / 1.2：
45.
図書
Setsuo Ichimaru
46.
図書
Josef Honerkamp
目次情報:
続きを見る
Statistical Physics Is More than Statistical Mechanics / 1：
Modeling of Statistical Systems / Part I：
Random Variables: Fundamentals of Probability Theory and Statistics / 2：
Probability and Random Variables / 2.1：
The Space of Events / 2.1.1：
Introduction of Probability / 2.1.2：
Random Variables / 2.1.3：
Multivariate Random Variables and Conditional Probabilities / 2.2：
Multidimensional Random Variables / 2.2.1：
Marginal Densities / 2.2.2：
Conditional Probabilities and Bayes' Theorem / 2.2.3：
Moments and Quantiles / 2.3：
Moments / 2.3.1：
Quantiles / 2.3.2：
The Entropy / 2.4：
Entropy for a Discrete Set of Events / 2.4.1：
Entropy for a Continuous Space of Events / 2.4.2：
Relative Entropy / 2.4.3：
Remarks / 2.4.4：
Applications / 2.4.5：
Computations with Random Variables / 2.5：
Addition and Multiplication of Random Variables / 2.5.1：
Further Important Random Variables / 2.5.2：
Limit Theorems / 2.5.3：
Stable Random Variables and Renormalization Transformations / 2.6：
Stable Random Variables / 2.6.1：
The Renormalization Transformation / 2.6.2：
Stability Analysis / 2.6.3：
Scaling Behavior / 2.6.4：
The Large Deviation Property for Sums of Random Variables / 2.7：
Random Variables in State Space: Classical Statistical Mechanics of Fluids / 3：
The Microcanonical System / 3.1：
Systems in Contact / 3.2：
Thermal Contact / 3.2.1：
Systems with Exchange of Volume and Energy / 3.2.2：
Systems with Exchange of Particles and Energy / 3.2.3：
Thermodynamic Potentials / 3.3：
Susceptibilities / 3.4：
Heat Capacities / 3.4.1：
Isothermal Compressibility / 3.4.2：
Isobaric Expansivity / 3.4.3：
Isochoric Tension Coefficient and Adiabatic Compressibility / 3.4.4：
A General Relation Between Response Functions / 3.4.5：
The Equipartition Theorem / 3.5：
The Radial Distribution Function / 3.6：
Approximation Methods / 3.7：
The Virial Expansion / 3.7.1：
Integral Equations for the Radial Distribution Function / 3.7.2：
Perturbation Theory / 3.7.3：
The van der Waals Equation / 3.8：
The Isotherms / 3.8.1：
The Maxwell Construction / 3.8.2：
Corresponding States / 3.8.3：
Critical Exponents / 3.8.4：
Some General Remarks about Phase Transitions and Phase Diagrams / 3.9：
Random Fields: Textures and Classical Statistical Mechanics of Spin Systems / 4：
Discrete Stochastic Fields / 4.1：
Markov Fields / 4.1.1：
Gibbs Fields / 4.1.2：
Equivalence of Gibbs and Markov Fields / 4.1.3：
Examples of Markov Random Fields / 4.2：
Model with Independent Random Variables / 4.2.1：
Auto Model / 4.2.2：
Multilevel Logistic Model / 4.2.3：
Gauss Model / 4.2.4：
Characteristic Quantities of Densities for Random Fields / 4.3：
Simple Random Fields / 4.4：
The White Random Field or the Ideal Paramagnetic System / 4.4.1：
The One-Dimensional Ising Model / 4.4.2：
Random Fields with Phase Transitions / 4.5：
The Curie-Weiss Model / 4.5.1：
The Mean Field Approximation / 4.5.2：
The Two-Dimensional Ising Model / 4.5.3：
The Landau Free Energy / 4.6：
The Renormalization Group Method for Random Fields and Scaling Laws / 4.7：
Scaling Laws / 4.7.1：
Time-Dependent Random Variables: Classical Stochastic Processes / 5：
Markov Processes / 5.1：
The Master Equation / 5.2：
Examples of Master Equations / 5.3：
Analytic Solutions of Master Equations / 5.4：
Equations for the Moments / 5.4.1：
The Equation for the Characteristic Function / 5.4.2：
Examples / 5.4.3：
Simulation of Stochastic Processes and Fields / 5.5：
The Fokker-Planck Equation / 5.6：
Fokker-Planck Equation with Linear Drift Term and Additive Noise / 5.6.1：
The Linear Response Function and the Fluctuation-Dissipation Theorem / 5.7：
The [Omega] Expansion / 5.8：
The One-Particle Picture / 5.8.2：
More General Stochastic Processes / 5.9：
Self-Similar Processes / 5.9.1：
Fractal Brownian Motion / 5.9.2：
Stable Levy Processes / 5.9.3：
Autoregressive Processes / 5.9.4：
Quantum Random Systems / 6：
Quantum-Mechanical Description of Statistical Systems / 6.1：
Ideal Quantum Systems: General Considerations / 6.2：
Expansion in the Classical Regime / 6.2.1：
First Quantum-Mechanical Correction Term / 6.2.2：
Relations Between the Thermodynamic Potential and Other System Variables / 6.2.3：
The Ideal Fermi Gas / 6.3：
The Fermi-Dirac Distribution / 6.3.1：
Determination of the System Variables at Low Temperatures / 6.3.2：
Applications of the Fermi-Dirac Distribution / 6.3.3：
The Ideal Bose Gas / 6.4：
Particle Number and the Bose-Einstein Distribution / 6.4.1：
Bose-Einstein Condensation / 6.4.2：
Pressure / 6.4.3：
Energy and Specific Heat / 6.4.4：
Entropy / 6.4.5：
Applications of Bose Statistics / 6.4.6：
The Photon Gas and Black Body Radiation / 6.5：
The Kirchhoff Law / 6.5.1：
The Stefan-Boltzmann Law / 6.5.2：
The Pressure of Light / 6.5.3：
The Total Radiative Power of the Sun / 6.5.4：
The Cosmic Background Radiation / 6.5.5：
Lattice Vibrations in Solids: The Phonon Gas / 6.6：
Systems with Internal Degrees of Freedom: Ideal Gases of Molecules / 6.7：
Magnetic Properties of Fermi Systems / 6.8：
Diamagnetism / 6.8.1：
Paramagnetism / 6.8.2：
Quasi-particles / 6.9：
Models for the Magnetic Properties of Solids / 6.9.1：
Superfluidity / 6.9.2：
Changes of External Conditions / 7：
Reversible State Transformations, Heat, and Work / 7.1：
Cyclic Processes / 7.2：
Exergy and Relative Entropy / 7.3：
Time Dependence of Statistical Systems / 7.4：
Analysis of Statistical Systems / Part II：
Estimation of Parameters / 8：
Samples and Estimators / 8.1：
Confidence Intervals / 8.2：
Propagation of Errors / 8.3：
The Maximum Likelihood Estimator / 8.4：
The Least-Squares Estimator / 8.5：
Signal Analysis: Estimation of Spectra / 9：
The Discrete Fourier Transform and the Periodogram / 9.1：
Filters / 9.2：
Filters and Transfer Functions / 9.2.1：
Filter Design / 9.2.2：
Consistent Estimation of Spectra / 9.3：
Frequency Distributions for Nonstationary Time Series / 9.4：
Filter Banks and Discrete Wavelet Transformations / 9.5：
Wavelets / 9.6：
Wavelets as Base Functions in Function Spaces / 9.6.1：
Wavelets and Filter Banks / 9.6.2：
Solutions of the Dilation Equation / 9.6.3：
Estimators Based on a Probability Distribution for the Parameters / 10：
Bayesian Estimator and Maximum a Posteriori Estimator / 10.1：
Marginalization of Nuisance Parameters / 10.2：
Numerical Methods for Bayesian Estimators / 10.3：
Identification of Stochastic Models from Observations / 11：
Hidden Systems / 11.1：
The Maximum a Posteriori (MAP) Estimator for the Inverse Problem / 11.2：
The Least-Squares Estimator as a Special MAP Estimator / 11.2.1：
Strategies for Choosing the Regularization Parameter / 11.2.2：
The Regularization Method / 11.2.3：
Examples of Estimating a Distribution Function by a Regularization Method / 11.2.4：
Estimating the Realization of a Hidden Process / 11.3：
The Viterbi Algorithm / 11.3.1：
The Kalman Filter / 11.3.2：
Estimating the Parameters of a Hidden Stochastic Model / 12：
The Expectation Maximization Method (EM Method) / 12.1：
Use of the EM Method for Estimation of the Parameters in Hidden Systems / 12.2：
Estimating the Parameters of a Hidden Markov Model / 12.3：
The Forward Algorithm / 12.3.1：
The Backward Algorithm / 12.3.2：
The Estimation Formulas / 12.3.3：
Estimating the Parameters in a State Space Model / 12.4：
Statistical Tests and Classification Methods / 13：
General Comments Concerning Statistical Tests / 13.1：
Test Quantity and Significance Level / 13.1.1：
Empirical Moments for a Test Quantity: The Bootstrap Method / 13.1.2：
The Power of a Test / 13.1.3：
Some Useful Tests / 13.2：
The z- and the t-Test / 13.2.1：
Test for the Equality of the Variances of Two Sets of Measurements, the F-Test / 13.2.2：
The x[superscript 2]-Test / 13.2.3：
The Kolmogorov-Smirnov Test / 13.2.4：
The F-Test for Least-Squares Estimators / 13.2.5：
The Likelihood-Ratio Test / 13.2.6：
Classification Methods / 13.3：
Classifiers / 13.3.1：
Estimation of Parameters That Arise in Classifiers / 13.3.2：
Automatic Classification (Cluster Analysis) / 13.3.3：
Random Number Generation for Simulating Realizations of Random Variables / Appendix：
Problems
Hints and Solutions
References
Index
Statistical Physics Is More than Statistical Mechanics / 1：
Modeling of Statistical Systems / Part I：
Random Variables: Fundamentals of Probability Theory and Statistics / 2：
47.
図書
Klaus R. Mecke, Dietrich Stoyan (eds.)
目次情報:
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Spatial Statistics and Point Processes: Basic Ideas of Spatial Statistics / I：
Stationary Models in Stochastic Geometry
Statistical Analysis of Large-Scale Strucutre in the Universe
Dynamics of Stucture Formation in Thin Film Liquid Films
Integral Geometry and Morphology of Patterns: Mixed Measures and Inhomogeneous Boolean Models / II：
Additivity, Convexity, and Beyond
Considerations About the Estimation of the Size Distribution in Wicksell's Corpuscule Problem
Local Porosity Theory and Stochastic Reconstruction for Porous Media
Stochastic Models as Tools for the Analysis of Decomposition and Crystallisation Phenomena in Solids
Phase Transitions and Simulations of Hard Particles: Phase Transition and Percolation in Gibbsian Particle Models / III：
Fun with Hard Spheres
Finite Packings and Parametric Density
A Primer on Perfect Simulation
Grand Canonical Simulations of Hard-Disk Systems by Simulated Tempering
Dynamics Triangulations for Granular Media Simulations
Spatial Statistics and Point Processes: Basic Ideas of Spatial Statistics / I：
Stationary Models in Stochastic Geometry
Statistical Analysis of Large-Scale Strucutre in the Universe
48.
図書
Nandita Rudra, P. Rudra
出版情報:
Hackensack : World Scientific, c2010 xvii, 229 p. ; 24 cm
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目次情報:
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Preface
Notations and Fundamental Constants
Basic Concepts / 1：
Introduction / 1.1：
Master Equation and Hypothesis of Equal á-priori Probability / 1.2：
Example of 3 Level Systems / 1.2.1：
Phase Space, Phase Point, Phase Trajectory / 1.3：
Statistical Distribution Function and Ergodic Hypothesis / 1.4：
Statistical Fluctuation and Statistical Independence / 1.5：
Statistical Fluctuation and Generalized Susceptibility / 1.6：
Generalized Ornstein-Zernicke Relation / 1.7：
Problems / 1.8：
Motion of Systems in Phase Space / 2：
Integral Invariants / 2.1：
Classical Liouville's Equation / 2.2：
Role of Energy / 2.3：
Quantum Mechanical Density Matrix / 2.4：
Quantum Liouville's Equation / 2.5：
States in Statistical Physics / 2.6：
Microscopic and Macroscopic States / 3.1：
Statistical Weight and Density of States / 3.2：
Examples: Non-interacting One- and N-Particle Systems and Spin-1/2 Particles / 3.3：
Entropy and Boltzmann's Principle / 3.4：
Boltzmann's H-Theorem / 3.5：
Statistical Ensembles / 3.6：
Microcanonical Distribution Function / 4.1：
Canonical (Gibbs) Distribution Function / 4.3：
Thermodynamic Temperature and Distribution Function / 4.3.1：
Spin-1/2 Particles and Negative Temperature / 4.3.2：
Partition Function and Different Thermodynamic Functions / 4.3.3：
System of Linear Harmonic Oscillators in Canonical Ensemble / 4.3.4：
Energy Fluctuation in Canonical Ensemble and Equivalence of Canonical and Microcanonical Ensembles / 4.3.5：
Grandcanonical Distribution Function / 4.4：
Dependence of Thermodynamic Functions on Number of Particles / 4.4.1：
Chemical Potential and Distribution Function / 4.4.2：
Density Fluctuation in Grandcanonical Ensemble and Equivalence of Grandcanonical and Canonical Ensembles / 4.4.3：
Ideal Gas / 4.5：
Boltzmann Distribution / 5.1：
Partition Function, Free Energy and Equation of State / 5.2：
Specific Heat: Translational, Vibrational and Rotational Components / 5.3：
Degeneracy Temperature / 5.4：
Chemical Reaction Equilibrium / 5.5：
Conditions of Chemical Equilibrum / 6.1：
Law of Mass Action / 6.2：
Heat of Reaction and Direction of Reaction / 6.3：
Ionization Equilibrium / 6.4：
Saha Formula / 6.5：
Real Gas / 6.6：
Free Energy, Virial Equation of State / 7.1：
Second Virial Coefficient and Applicability of Virial Equation / 7.2：
Model Calculation and van-der-Waal's Equation of State / 7.3：
Joule-Thomson Expansion and Inversion Temperature / 7.4：
Strong Electrolytes / 7.5：
Debye-Hückel Approximation, Debye Length / 8.1：
Screened Coulomb Potential / 8.2：
Equation of State and Osmotic Pressure / 8.3：
Quantum Statistics / 8.4：
Bose and Fermi Distributions / 9.1：
Quantum Gases of Elementary Particles: Number Density and Chemical Potential, Energy Density, Equation of State / 9.2：
Black Body Radiation and Planck's Law / 9.3：
Lattice Specific Heat and Phonons / 9.4：
Degenerate Bose Gas, Bose Condensation / 9.5：
Liquid He and Superfluidity / 9.6：
Systematics of Liquid 4 He / 9.6.1：
Landau's 2-Fluid Model / 9.6.2：
Systematics of Liquid 3 He / 9.6.3：
Degenerate Fermi Gas, Degeneracy Pressure, Specific Heat / 9.7：
Magnetism of Free Fermions / 9.8：
Preamble / 9.8.1：
Landau Diamagnetism / 9.8.2：
Pauli Paramagnetism / 9.8.3：
Interacting Fermi System: Fermi Liquid Theory / 9.9：
Relativistic Degenerate Fermi Gas / 9.10：
Bose-Einstein Condensate / 9.11：
Trapping of Atoms / 10.1：
Cooling of Atoms / 10.3：
Statistical Astrophysics / 10.4：
Stars: Stability and Evolution / 11.1：
High Temperature Dense Matter / 11.3：
Neutron Stars and Black Holes / 11.4：
Phase Transitions / 11.5：
Systematics of Phase Transitions / 12.1：
Ehrenfest's Classification of Phase Transitions / 12.2：
Order Parameter, Continuous and Discontinuous Transitions / 12.3：
Landau's Theory of Continuous Phase Transitions / 12.4：
Continuity of Entropy and Discontinuity of Specific Heat / 12.5：
Generalized Susceptibility / 12.6：
Critical Exponents and Fluctuations of Order Parameter / 12.7：
Ising Model / 12.8：
Zero-Field 1-Dimensional Case / 12.8.1：
Non-Zero-Field 1-Dimensional Case / 12.8.2：
Multi-Dimensional Case / 12.8.3：
2-Dimensional Ising System / 12.8.4：
Irreversible Processes / 12.9：
Linear Response Theory (Kubo Formalism) / 13.1：
Mechanical Process / 13.2.1：
Thermal Process / 13.2.2：
Symmetry Relations / 13.3：
Fluctuation-Dissipation Theorem / 13.4：
Mathematical Appendix / 13.5：
Beta and Gamma Functions / 14.1：
Dirac Delta Function (Distribution) / 14.2：
Functional Derivative / 14.3：
Mathematical Identities / 14.4：
Multiple Summation / 14.5：
Pauli Matrices / 14.6：
Probability Theory / 14.7：
Elementary Results of Probability Theory / 14.7.1：
Statistical Distributions / 14.7.2：
Central Limit Theorem / 14.7.3：
Quantum Mechanics, A Retrospect / 14.8：
Riemann, Bernoulli and Fourier / 14.9：
Riemann's ζ-Function / 14.9.1：
Bernoulli Numbers and Polynomials / 14.9.2：
Fourier Series / 14.9.3：
Integrals of Quantum Statistics / 14.9.4：
Sanskrit Transliteration / 14.10：
Stirling's Theorem / 14.11：
Summation and Integration / 14.12：
Volume of an N-Dimensional Sphere / 14.13：
Bibliography
Index
Preface
Notations and Fundamental Constants
Basic Concepts / 1：
49.
図書
Harvey Gould and Jan Tobochnik
出版情報:
Princeton, N.J. : Princeton University Press, c2010 xvii, 511 p. ; 24 cm
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50.
図書
Kurt Binder, Dieter W. Heermann
51.
図書
Rosario N. Mantegna, H. Eugene Stanley
出版情報:
Cambridge, U.K. : Cambridge University Press, 2000 ix, 148 p. ; 26 cm
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Preface
Introduction / 1：
Efficient market hypothesis / 2：
Random walk / 3：
Lévy stochastic processes and limit theorems / 4：
Scales in financial data / 5：
Stationarity and time correlation / 6：
Time correlation in financial time series / 7：
Stochastic models of price dynamics / 8：
Scaling and its breakdown / 9：
ARCH and GARCH processes / 10：
Financial markets and turbulence / 11：
Correlation and anti-correlation between stocks / 12：
Taxonomy of a stock portfolio / 13：
Options in idealized markets / 14：
Options in real markets / 15：
Notation guide / Appendix A：
Martingales / Appendix B：
References
Index
LFvy stochastic processes and limit theorems
Preface
Introduction / 1：
Efficient market hypothesis / 2：
52.
図書
[by] A. Isihara
出版情報:
New York ; London : Academic Press, c1971 xv, 438 p. ; 24 cm
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53.
図書
by E.M. Lifshitz and L.P. Pitaevskiĭ ; translated from the Russian by J.B. Sykes and M.J. Kearsley
目次情報:
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Fundamental principles of theoretical physics
The Gibbs distribution
Ideal gases
Solids
Non-ideal gases
Solutions
Chemical reactions
Fluctuations
Surfaces
Fundamental principles of theoretical physics
The Gibbs distribution
Ideal gases
54.
図書
Bernard H. Lavenda
出版情報:
New York : Wiley, c1991 xii, 371 p. ; 25 cm
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Entropy and Probability
Black Radiation: A Case History
From One to Infinity
Processing Information
Origins of the Canonical Distribution
Statistical Equivalence Principle
Radiative and Material Phase Transitions
Kinetic Foundations of Gauss' Error Law
Index
Entropy and Probability
Black Radiation: A Case History
From One to Infinity
55.
図書
by L.D. Landau and E.M. Lifshitz ; translated from the Russian by J.B. Sykes and M.J. Kearsley
目次情報:
続きを見る
Fundamental principles of theoretical physics
The Gibbs distribution
Ideal gases
Solids
Non-ideal gases
Solutions
Chemical reactions
Fluctuations
Surfaces
Fundamental principles of theoretical physics
The Gibbs distribution
Ideal gases
56.
図書
edited by K. Binder ; with contributions by A. Baumgärtner ... [et al.]
57.
図書
editor, P. T. Landsberg
出版情報:
London : Pion, c1971 [4], viii, 573 p. ; 24 cm
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58.
図書
M.E.J. Newman and G.T. Barkema
出版情報:
Oxford [Oxfordshire] : Clarendon Press, 1999 xiv, 475 p. ; 24 cm
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Equilibrium Monte Carlo calculations / I：
Introduction / 1：
The principles of equilibrium thermal Monte Carlo simulations / 2：
The Ising model and the Metropolis algorithm / 3：
Other algorithms for the Ising model / 4：
The conserved-order-parameter Ising model / 5：
Disordered spin models / 6：
Ice models / 7：
Analysing Monte Carlo data / 8：
Out-of-equilibrium calculations / II：
Principles of out-of-equilibrium Monte Carlo simulation / 9：
Non-equilibrium simulations of the Ising model / 10：
Monte Carlo simulations in surface science / 11：
The repton model / 12：
Implementation / III：
Lattices and data structures / 13：
Monte Carlo simulations on parallel computers / 14：
Multispin coding / 15：
Random numbers / 16：
Equilibrium Monte Carlo calculations / I：
Introduction / 1：
The principles of equilibrium thermal Monte Carlo simulations / 2：
59.
図書
東工大
Hidetoshi Nishimori
目次情報:
続きを見る
1 Mean-field theory of phase transitions 1
1.1 Ising model 1
1.2 Order parameter and phase transition 3
1.3 Mean-field theory 4
1.3.1 Mean-field Hamiltonian 4
1.3.2 Equation of state 5
1.3.3 Free energy and the Landau theory 6
1.4 Infinite-range model 7
1.5 Variational approach 9
2 Mean-field theory of spin glasses 11
2.1 Spin glass and the Edwards-Anderson model 11
2.1.1 Edwards-Anderson model 12
2.1.2 Quenched system and configurational average 12
2.1.3 Replica method 13
2.2 Sherrington-Kirkpatrick model 13
2.2.1 SK model 14
2.2.2 Replica average of the partition function 14
2.2.3 Reduction by Gaussian integral 15
2.2.4 Steepest descent 15
2.2.5 Order parameters 16
2.3 Replica-symmetric solution 17
2.3.1 Equations of state 17
2.3.2 Phase diagram 19
2.3.3 Negative entropy 21
3 Replica symmetry breaking 23
3.1 Stability of replica-symmetric solution 23
3.1.1 Hessian 24
3.1.2 Eigenvalues of the Hessian and the AT line 26
3.2 Replica symmetry breaking 27
3.2.1 Parisi solution 28
3.2.2 First-step RSB 29
3.2.3 Stability of the first-step RSB 31
3.3 Full RSB solution 31
3.3.1 Physical quantities 31
3.3.2 Order parameter near the critical point 32
3.3.3 Vertical phase boundary 33
3.4 Physical significance of RSB 35
3.4.1 Multivalley structure 35
3.4.2 qEA and q 35
3.4.3 Distribution of overlaps 36
3.4.4 Replica representation of the order parameter 37
3.4.5 Ultrametricity 38
3.5 TAP equation 38
3.5.1 TAP equation 39
3.5.2 Cavity method 41
3.5.3 Properties of the solution 43
4 Gauge theory of spin glasses 46
4.1 Phase diagram of finite-dimensional systems 46
4.2 Gauge transformation 47
4.3 Exact solution for the internal energy 48
4.3.1 Application of gauge transformation 48
4.3.2 Exact internal energy 49
4.3.3 Relation with the phase diagram 50
4.3.4 Distribution of the local energy 51
4.3.5 Distribution of the local field 51
4.4 Bound on the specific heat 52
4.5 Bound on the free energy and internal energy 53
4.6 Correlation functions 55
4.6.1 Identities 55
4.6.2 Restrictions on the phase diagram 57
4.6.3 Distribution of order parameters 58
4.6.4 Non-monotonicity of spin configurations 61
4.7 Entropy of frustration 62
4.8 Modified ±J model 63
4.8.1 Expectation value of physical quantities 63
4.8.2 Phase diagram 64
4.8.3 Existence of spin glass phase 65
4.9 Gauge glass 67
4.9.1 Energy, specific heat, and correlation 67
4.9.2 Chirality 69
4.9.3 XY spin glass 70
4.10 Dynamical correlation function 71
5 Error-correcting codes 74
5.1 Error-correcting codes 74
5.1.1 Transmission of information 74
5.1.2 Similarity to spin glasses 75
5.1.3 Shannon bound 76
5.1.4 Finite-temperature decoding 78
5.2 Spin glass representation 78
5.2.1 Conditional probability 78
5.2.2 Bayes formula 79
5.2.3 MAP and MPM 80
5.2.4 Gaussian channel 81
5.3 Overlap 81
5.3.1 Measure of decoding performance 81
5.3.2 Upper bound on the overlap 82
5.4 Infinite-range model 83
5.4.1 Infinite-range model 84
5.4.2 Replica calculations 84
5.4.3 Replica-symmetric solution 86
5.4.4 Overlap 87
5.5 Replica symmetry breaking 88
5.5.1 First-step RSB 88
5.5.2 Random energy model 89
5.5.3 Replica solution in the limit γ→∞ 91
5.5.4 Solution for finite γ 93
5.6 Codes with finite connectivity 95
5.6.1 Sourlas-type code with finite connectivity 95
5.6.2 Low-density parity-check code 98
5.6.3 Cryptography 101
5.7 Convolutional code 102
5.7.1 Definition and examples 102
5.7.2 Generating polynomials 103
5.7.3 Recursive convolutional code 104
5.8 Turbo code 106
5.9 CDMA multiuser demodulator 108
5.9.1 Basic idea of CDMA 108
5.9.2 Conventional and Bayesian demodulators 110
5.9.3 Replica analysis of the Bayesian demodulator 111
5.9.4 Performance comparison 114
6 Image restoration 116
6.1 Stochastic approach to image restoration 116
6.1.1 Binary image and Bayesian inference 116
6.1.2 MAP and MPM 117
6.1.3 Overlap 118
6.2 Infinite-range model 119
6.2.1 Replica calculations 119
6.2.2 Temperature dependence of the overlap 121
6.3 Simulation 121
6.4 Mean-field annealing 122
6.4.1 Mean-field approximation 123
6.4.2 Annealing 124
6.5 Edges 125
6.6 Parameter estimation 128
7 Associative memory 131
7.1 Associative memory 131
7.1.1 Model neuron 131
7.1.2 Memory and stable fixed point 132
7.1.3 Statistical mechanics of the random Ising model 133
7.2 Embedding a finite number of patterns 135
7.2.1 Free energy and equations of state 135
7.2.2 Solution of the equation of state 136
7.3 Many patterns embedded 138
7.3.1 Replicated partition function 138
7.3.2 Non-retrieved patterns 138
7.3.3 Free energy and order parameter 140
7.3.4 Replica-symmetric solution 141
7.4 Self-consistent signal-to-noise analysis 142
7.4.1 Stationary state of an analogue neuron 142
7.4.2 Separation of signal and noise 143
7.4.3 Equation of state 145
7.4.4 Binary neuron 145
7.5 Dynamics 146
7.5.1 Synchronous dynamics 147
7.5.2 Time evolution of the overlap 147
7.5.3 Time evolution of the variance 148
7.5.4 Limit of applicability 150
7.6 Perceptron and volume of connections 151
7.6.1 Simple perceptron 151
7.6.2 Perceptron learning 152
7.6.3 Capacity of a perceptron 153
7.6.4 Replica representation 154
7.6.5 Replica-symmetric solution 155
8 Learning in perceptron 158
8.1 Learning and generalization error 158
8.1.1 Learning in perceptron 158
8.1.2 Generalization error 159
8.2 Batch learning 161
8.2.1 Bayesian formulation 162
8.2.2 Learning algorithms 163
8.2.3 High-temperature and annealed approximations 165
8.2.4 Gibbs algorithm 166
8.2.5 Replica calculations 167
8.2.6 Generalization error at T=0 169
8.2.7 Noise and unlearnable rules 170
8.3 On-line learning 171
8.3.1 Learning algorithms 171
8.3.2 Dynamics of learning 172
8.3.3 Generalization errors for specific algorithms 173
8.3.4 Optimization of learning rate 175
8.3.5 Adaptive learning rate for smooth cost function 176
8.3.6 Learning with query 178
8.3.7 On-line learning of unlearnable rule 179
9 Optimization problems 183
9.1 Combinatorial optimization and statistical mechanics 183
9.2 Number partitioning problem 184
9.2.1 Definition 184
9.2.2 Subset sum 185
9.2.3 Number of configurations for subset sum 185
9.2.4 Number partitioning problem 187
9.3 Graph partitioning problem 188
9.3.1 Definition 188
9.3.2 Cost function 189
9.3.3 Replica expression 190
9.3.4 Minimum of the cost function 191
9.4 Knapsack problem 192
9.4.1 Knapsack problem and linear programming 192
9.4.2 Relaxation method 193
9.4.3 Replica calculations 193
9.5 Satisfiability problem 195
9.5.1 Random satisfiability problem 195
9.5.2 Statistical-mechanical formulation 196
9.5.3 Replica-symmetric solution and its interpretation 199
9.6 Simulated annealing 201
9.6.1 Simulated annealing 202
9.6.2 Annealing schedule and generalized transition probability 203
9.6.3 Inhomogeneous Markov chain 204
9.6.4 Weak ergodicity 206
9.6.5 Relaxation of the cost function 209
9.7 Diffusion in one dimension 211
9.7.1 Diffusion and relaxation in one dimension 211
A Eigenvalues of the Hessian 214
A.1 Eigenvalue 1 214
A.2 Eigenvalue 2 215
A.3 Eigenvalue 3 216
B Parisi equation 217
C Channel coding theorem 220
C.1 Information, uncertainty, and entropy 220
C.2 Channel capacity 221
C.3 BSC and Gaussian channel 223
C.4 Typical sequence and random coding 224
C.5 Channel coding theorem 226
D Distribution and free energy of K-SAT 228
References 232
Index 241
1 Mean-field theory of phase transitions 1
1.1 Ising model 1
1.2 Order parameter and phase transition 3
60.
図書
A.I. Akhiezer and S.V. Peletminskii ; translated by M. Schukin
61.
図書
edited by Elizabeth Garber, Stephen G. Brush, and C.W.F. Everitt
出版情報:
Cambridge, Mass. : MIT Press, c1986 xxvii, 565 p. ; 24 cm
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62.
図書
James Glimm, Arthur Jaffe
出版情報:
New York : Springer-Verlag, c1981 xx, 417 p. ; 24 cm
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63.
図書
S.W. Lovesey
64.
図書
Setsuo Ichimaru
65.
図書
by Yu.L. Klimontovich ; translated from the Russian by G. Pontecorvo
出版情報:
Chur, Switzerland ; New York : Harwood Academic Publishers, c1986 xxvi, 734 p. ; 24 cm
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66.
図書
edited by K. Binder, with contributions by A. Baumgärtner ... [et al.]
67.
図書
Harald J.W. Müller-Kirsten
出版情報:
Hackensack, N.J. : World Scientific, c2022 xvi, 254 p. ; 25 cm
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68.
図書
Daniel M. Zuckerman
出版情報:
Boca Raton, FL : CRC Press, Taylor & Francis, c2010 xxi, 334 p. ; 25 cm
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69.
図書
by L.D. Landau and E.M. Lifshitz ; translated from the Russian by J.B. Sykes and M.J. Kearsley
70.
図書
S.W. Lovesey
出版情報:
Reading, Mass. : Benjamin/Cummings Pub. Co., Advanced Book Program, 1980 xiii, 191 p. ; 25 cm
シリーズ名:
Frontiers in physics ; v. 49
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71.
図書
Claude Itzykson, Jean-Michel Drouffe
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Contents of Volume 1
Preface
Diagrammatic methods / 7：
General Techniques / 7.1：
Definitions and notations / 7.1.1：
Connected graphs and cumulants / 7.1.2：
Irreducibility and Legendre transformation / 7.1.3：
Series expansions / 7.2：
High temperature expansion / 7.2.1：
The role of symmetries / 7.2.2：
Low temperature expansion--discrete case / 7.2.3：
Low temperature expansion--continuous case / 7.2.4：
Strong field expansions / 7.2.5：
Fermionic fields / 7.2.6：
Enumeration of graphs / 7.3：
Configuration numbers with exclusion constraint / 7.3.1：
Multiply connected graphs / 7.3.2：
Results and analysis / 7.4：
Series analysis / 7.4.1：
An example: the Ising series on a body centered cubic lattice / 7.4.2：
Notes
Numerical simulations / 8：
Algorithms / 8.1：
Generalities / 8.1.1：
The classical algorithms / 8.1.2：
Microcanonical simulations / 8.1.3：
Practical considerations / 8.1.4：
Extraction of results in a simulation / 8.2：
Determination of transitions / 8.2.1：
Finite size effects / 8.2.2：
Monte Carlo renormalization group / 8.2.3：
Dynamics and the Langevin equation / 8.2.4：
Simulating fermions / 8.3：
The quenched approximation / 8.3.1：
Dynamical fermions / 8.3.2：
Hadron mass calculation in lattice gauge theory / 8.3.3：
Conformal invariance / 9：
Energy-momentum tensor--Virasoro algebra / 9.1：
Energy-momentum tensor / 9.1.1：
Two-dimensional conformal transformations / 9.1.3：
Central charge / 9.1.4：
Virasoro algebra / 9.1.5：
The Kac determinant / 9.1.6：
Unitary and minimal representations / 9.1.7：
Characters of the Virasoro algebra / 9.1.8：
Examples / 9.2：
Gaussian model / 9.2.1：
Ising model / 9.2.2：
Three state Potts model / 9.2.3：
Finite size effects and modular invariance / 9.3：
Partition functions on a torus / 9.3.1：
Kronecker's limit formula / 9.3.2：
The A-D-E classification of minimal models / 9.3.3：
Frustrations and discrete symmetries / 9.3.5：
Nonminimal models / 9.3.6：
Correlations in a half plane / 9.3.7：
The vicinity of the critical point / 9.3.8：
Jacobian [theta]-series and products / 9.A：
Superconformal algebra / 9.B：
Current algebra / 9.C：
Simple Lie algebras / 9.C.1：
The Wess-Zumino-Witten model / 9.C.2：
Representations and characters of KacMoody algebras / 9.C.3：
Disordered systems and fermionic methods / 10：
One-dimensional models / 10.1：
Gaussian random potential / 10.1.1：
Fokker-Planck equation / 10.1.2：
The replica trick / 10.1.3：
Random one-dimensional lattice / 10.1.4：
Two-dimensional electron gas in a strong field / 10.2：
Landau levels - Quantum Hall effect / 10.2.1：
One particle spectrum in the presence of impurities / 10.2.2：
Random matrices / 10.3：
Semicircle law / 10.3.1：
The fermionic method / 10.3.2：
Level spacings / 10.3.3：
The planar approximation / 10.4：
Combinatorics / 10.4.1：
The planar approximation in quantum mechanics / 10.4.2：
Spin systems with random interactions / 10.5：
Random external field and dimensional transmutation / 10.5.1：
The two-dimensional Ising model with random bonds / 10.5.2：
The Hall conductance as a topological invariant / 10.A：
Random geometry / 11：
Random lattices / 11.1：
Poissonian lattices and cell statistics / 11.1.1：
Field equations / 11.1.2：
The spectrum of the Laplacian / 11.1.3：
Random surfaces / 11.2：
Piecewise linear surfaces / 11.2.1：
The conformal anomaly and the Liouville action / 11.2.2：
Sums over smooth surfaces / 11.2.3：
Discretized models / 11.2.4：
Index
Disordered systems and Fermionic methods / 1：
Contents of Volume 1
Preface
Diagrammatic methods / 7：
72.
図書
Setsuo Ichimaru
73.
図書
Leo P. Kadanoff
出版情報:
Singapore : World Scientific, c2000 xiii, 483 p. ; 27 cm
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Introduction
Fundamentals of Statistical Physics / I：
The Lectures--A Survey / 1：
The Journey: Many Different Approaches / 1.1：
The Main Sights / 1.2：
Is the Trip Worthwhile? / 1.3：
One Particle and Many / 2：
Formulation / 2.1：
The Ising Model / 2.2：
N Independent Particles--Quantum Description / 2.3：
Averages From Derivatives / 2.4：
N Independent Particles in a Box / 2.5：
Fluctuations Big and Small / 2.6：
The Problems of Statistical Physics / 2.7：
Gaussian Distributions / 3：
One Variable / 3.1：
Many Gaussian Variables / 3.3：
Lattice Green Function / 3.4：
Gaussian Random Functions / 3.5：
Central Limit Theorem / 3.6：
Distribution of Energies / 3.7：
Large Deviations / 3.8：
On Almost Gaussian Integrals / 3.9：
Three Versions of Gaussian Problems / 3.10：
Quantum Mechanics and Lattices / 4：
All of Quantum Mechanics in One Brief Section / 4.1：
From d = 1 Models to Quantum Mechanics / 4.2：
An Example: The Linear Ising Chain / 4.3：
One-Dimensional Gaussian Model / 4.4：
Coherence Length / 4.5：
Operator Averages / 4.6：
Correlation Functions / 4.7：
Ising Correlations / 4.8：
Two-Dimensional Ising Model / 4.9：
Random Dynamics / II：
Diffusion and Hopping / 5：
Random Walk on a Lattice / 5.1：
Formulating This Problem / 5.2：
The Diffusion of Probability and Particles / 5.3：
From Conservation to Hydrodynamic Equations / 5.4：
Distribution Functions / 5.5：
Cascade Processes and Securities Prices / 5.6：
Reprints on Dynamics / 5.7：
Forest and Witten: Smoke Particle Aggregates / 5.7.1：
Witten and Sander: Diffusion Limited Aggregation / 5.7.2：
Kadanoff: Chaos and Complexity / 5.7.3：
From Hops to Statistical Mechanics / 6：
Random Walk in Momentum / 6.1：
The Diffusion Equation Again / 6.2：
Time Dependence of Probability / 6.3：
Time Dependence in Deterministic Case / 6.4：
Equilibrium Solutions / 6.5：
Back to Collisions / 6.6：
From Fokker-Planck to Equilibrium / 6.7：
Properties of Fokker-Planck Equation / 6.8：
Reprints on Organization / 6.9：
Chao Tang et al.: Phase Organization / 6.9.1：
Bak et al.: Self-Organized Criticality / 6.9.2：
Carlson et al.: Singular Diffusion / 6.9.3：
Jaeger et al.: Experimental Studies / 6.9.4：
Correlations and Response / 7：
Time Independent Response / 7.1：
Hamiltonian Time-Dependence / 7.2：
Sum Rules / 7.3：
Non-Interacting Particles / 7.4：
Plasma Behavior / 7.5：
More Statistical Mechanics / III：
Statistical Thermodynamics / 8：
The Chemical Potential Defined / 8.1：
Barometer Formula / 8.2：
Sharing Energy / 8.3：
Ensemble Theory / 8.4：
Temperatures and Energy Flow / 8.5：
Fermi, Bose, and Other / 9：
Quantum Formulation / 9.1：
Statistical Mechanics of Non-Interacting Degenerate Particles / 9.2：
The Non-Degenerate Limit / 9.3：
Degenerate Fermions / 9.4：
Degenerate Bosons I. Photons and Phonons / 9.5：
Degenerate Bosons II. One-Dimensional Phonons / 9.6：
Degenerate Bosons III. Bose Phase Transition / 9.7：
Entropies / 9.8：
Phase Transitions / IV：
Overview of Phase Transitions / 10：
Thermodynamic Phases / 10.1：
Two Kinds of Transitions / 10.2：
Back to the Ising Model / 10.4：
Mean Field Theory of Magnets / 10.5：
The Phases / 10.6：
Low Temperature Result / 10.7：
Free Energy Selection Argument / 10.8：
Behaviors of Different Phases / 10.9：
Mean Field Theory of Critical Behavior / 11：
The Infinite Range Model / 11.1：
Mean Field Theory Near the Critical Point / 11.2：
Critical Indices / 11.3：
Scaling Function for Magnetization / 11.4：
Spatial Correlations / 11.5：
Analyticity / 11.6：
Mean Field Theory for the Free Energy / 11.7：
When Mean Field Theory Fails / 11.8：
Continuous Phase Transitions / 12：
Historical Background / 12.1：
Widom Scaling Theory / 12.2：
The Ising Model: Rescaled / 12.3：
Fixed Points / 12.4：
Phenomenology of Scaling Fields / 12.5：
Theory of Scaling Fields / 12.6：
Scaling Relations for Operators / 12.7：
Transforming Operators / 12.8：
Universality / 12.9：
Operator Product Expansions / 12.10：
Reprints on Critical Correlations / 12.11：
Kadanoff: Correlations Along a Line / 12.11.1：
Kadanoff-Wegner: Marginal Behavior / 12.11.2：
Renormalization in One Dimension / 13：
Decimation / 13.1：
The Ising Example / 13.3：
Phase Diagrams, Flow Diagrams, and the Coherence Length / 13.4：
The Gaussian Model / 13.5：
Analysis of Recursion Relation / 13.6：
Fixed Point Analysis for the Gaussian Model / 13.7：
Real Space Renormalization Techniques / 13.8：
Decimation: An Exact Calculation / 14.1：
The Method of Neglect / 14.3：
Potential Moving / 14.4：
Further Work / 14.5：
Reprints on Real Space RG / 14.6：
Niemeijer and van Leeuwen: Triangular Lattice R.G. / 14.6.1：
David Nelson's Early Summary / 14.6.2：
Kadanoff: Bond-moving, and a Variational Method / 14.6.3：
Kadanoff: Migdal's Simple and Versatile Method / 14.6.4：
Migdal's Original Papers / 14.6.5：
Duality / 15：
Doing Sums / 15.1：
Two Dimensions / 15.2：
Direct Coupling and Dual Coupling / 15.3：
Two-Dimensional Calculation / 15.4：
Ising Model / 15.5：
XY is Connected to SOS / 15.6：
Gaussian goes into Gaussian / 15.7：
Dual Correlations / 15.8：
Planar Model and Coulomb Systems / 16：
Why Study a Planar Model? / 16.1：
One-Dimensional Case / 16.2：
Phases of the Planar Model / 16.3：
The Gaussian Approximation / 16.4：
Two-Dimensional Coulomb Systems / 16.5：
Multipole Expansion / 16.6：
Reprint on Spin Waves / 16.7：
V. L. Berezinskii: An Overview of Problems with Continuous Symmetry / 16.7.1：
XY Model, Renormalization, and Duality / 17：
Plan of Action / 17.1：
Villain Representation of the Basic Bonds / 17.2：
Duality Transformation / 17.3：
Two Limits / 17.4：
Vortex Representation / 17.5：
The Magnetically Charged System / 17.6：
Correlation Calculation / 17.7：
The Renormalization Calculation / 17.8：
Spatial Averages / 17.9：
The Actual Renormalization / 17.10：
Reprints on Planar Model / 17.11：
The Kosterlitz-Thouless Theory / 17.11.1：
Kosterlitz: On Renormalization of the Planar Model / 17.11.2：
Jorge V. Jose, Leo P. Kadanoff, Scott Kirkpatrick, David R. Nelson: Renormalization and Vortices / 17.11.3：
Index
Introduction
Fundamentals of Statistical Physics / I：
The Lectures--A Survey / 1：
74.
図書
editors, Mikio Nakahara, Shu Tanaka
目次情報:
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Preface
Symposium
List of Participants
Organizing Committee
Bosons in an Optical Lattice with a Synthetic Magnetic Field / K. Kasamatsu
Quantum Simulation Using Exciton-Polaritons and their Applications Toward Accelerated Optimization Problem Search / T. Byrnes ; K. Yan ; K. Kusudo ; M. Fraser ; Y. Yamamoto
Quantum Simulation Using Ultracold Atoms in Optical Lattices / S. Sugawa ; S. Taie ; R. Yamazaki ; Y. Takahashi
Universality of Integrable Model: Baxter's T-Q Equation, SU(N)/SU(2)N-3 Correspondence and Ω-Deformed Seiberg-Witten Prepotential / T.-S. Tai
Exact Analysis of Correlation Functions of the XXZ Chain / T. Deguchi ; K. Motegi ; J. Sato
Classical Analogue of Weak Value in Stochastic Process / H. Tomita
Scaling of Entanglement Entropy and Hyperbolic Geometry / H. Matsueda
From Classical Neural Networks to Quantum Neural Networks / B. Tirozzi
Analysis of Quantum Monte Carlo Dynamics in Infinite-range Ising Spin Systems: Theory and Its Possible Applications / J. Inoue
A Method to Control Order of Phase Transition: Invisible States in Discrete Spin Models / R. Tamura ; S. Tanaka ; N. Kawashima
Quantum Annealing and Quantum Fluctuation Effect in Frustrated Ising Systems
Preface
Symposium
List of Participants
75.
図書
Claude Itzykson, Jean-Michel Drouffe
目次情報:
続きを見る
Contents of Volume 2
Preface
From Brownian motion to Euclidean fields / 1：
Brownian motion / 1.1：
Random walks / 1.1.1：
The sum over paths / 1.1.2：
The dimension two of Brownian curves / 1.1.3：
Euclidean fields / 1.2：
Free fields / 1.2.1：
Interacting fields and random walks / 1.2.2：
Self-avoiding walks and the limit n [right arrow] 0 / 1.2.3：
Comparison with the high temperature expansion / 1.2.4：
The one-dimensional case / 1.2.5：
Lattices / 1.A：
Notes
Grassmannian integrals and the two-dimensional Ising model / 2：
Grassmannian integrals / 2.1：
Anticommuting variables / 2.1.1：
Integrals / 2.1.2：
The two-dimensional Ising model / 2.2：
Duality / 2.2.1：
Transfer matrix / 2.2.2：
Fermionic representation / 2.2.3：
Free energy / 2.2.4：
Spontaneous magnetization / 2.2.5：
Correlation function in the high temperature phase / 2.2.6：
Surface tension / 2.2.7：
Critical continuous theory / 2.3：
Effective action / 2.3.1：
Correlation functions / 2.3.2：
Quadratic differences and Painleve equations / 2.A：
Spontaneous symmetry breaking, mean field / 3：
Mean field approximation / 3.1：
Dielectric constant of a polarizable medium / 3.1.1：
Classical spin model with a finite symmetry group / 3.1.2：
Continuous symmetry group / 3.1.3：
The Bethe approximation / 3.1.4：
Critical exponents / 3.1.5：
Lee-Yang zeroes / 3.2：
The Lee-Yang theorem / 3.2.1：
General properties / 3.2.2：
Zeroes in the temperature plane / 3.2.4：
Large n limit / 3.3：
Saddle point method / 3.3.1：
Factorization / 3.3.2：
Coupling to an external field / 3.3.3：
Corrections to mean field / 3.4：
Laplace transform / 3.4.1：
Scaling transformations and the XY-model / 4：
Scaling laws. Real space renormalization / 4.1：
Homogeneity and scale invariance / 4.1.1：
Recurrence relations in real space / 4.1.2：
Examples and approximations / 4.1.3：
The XY-model / 4.2：
High temperature behaviour / 4.2.1：
Low temperature expansion. Vortices / 4.2.2：
The Villain action / 4.2.3：
Correlations / 4.2.4：
Renormalization flow / 4.2.5：
Two-dimensional systems with continuous symmetry / 4.A：
Magnetization inequality / 4.A.1：
Correlation inequality / 4.A.2：
Phenomenological renormalization / 4.B：
Continuous field theory and the renormalization group / 5：
The Lagrangian and dimensional analysis / 5.1：
Introduction / 5.1.1：
Generating functionals and dimensional analysis / 5.1.2：
The perturbative method / 5.2：
Diagrammatic series / 5.2.1：
Loop expansion / 5.2.2：
Evaluation of integrals and dimensional continuation / 5.2.3：
Group theoretical factors / 5.2.4：
Power counting / 5.2.5：
Perturbative renormalization / 5.2.6：
The renormalization group / 5.3：
From the Gaussian ultraviolet fixed point to the infrared critical point in dimension less than four / 5.3.1：
Correlation functions at the critical point / 5.3.4：
Expansion near the critical point / 5.3.5：
Scaling laws below the critical temperature / 5.3.6：
Corrections to scaling laws / 5.4：
Deviation from the critical point in dimension lower than four / 5.4.1：
Logarithmic corrections in dimension four / 5.4.2：
Irrelevant operators / 5.4.3：
Numerical results / 5.5：
[varepsilon]-expansion of critical exponents / 5.5.1：
Equation of state / 5.5.2：
Amplitude ratios / 5.5.3：
Three-dimensional results / 5.5.4：
Multicritical points / 5.A：
Lattice gauge fields / 6：
Generalities / 6.1：
Presentation / 6.1.1：
The continuous limit / 6.1.2：
Order parameter and Elitzur's theorem / 6.1.3：
Structure of the phase diagram / 6.1.4：
Corrections to mean field and restoration of gauge invariance / 6.2.1：
Discrete groups: 1/d expansion / 6.2.3：
Continuous groups: computation of corrections / 6.2.4：
Strong coupling expansions / 6.3：
Convergence / 6.3.1：
Character expansions / 6.3.2：
String tension and roughening transition / 6.3.3：
Mass spectrum / 6.3.5：
Lattice fermions / 6.4：
The doubling problem / 6.4.1：
The Nielsen-Ninomiya theorem / 6.4.2：
Staggered fermions / 6.4.3：
Index
Grassmannian integrals and two-dimensional Ising models
Spontaneous symmetry breaking
Contents of Volume 2
Preface
From Brownian motion to Euclidean fields / 1：
76.
図書
David P. Landau, Kurt Binder
出版情報:
Cambridge : Cambridge University Press, 2005 xv, 432 p. ; 26 cm
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目次情報:
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Introduction / 1：
Some necessary background / 2：
Simple sampling Monte Carlo methods / 3：
Importance sampling Monte Carlo methods / 4：
More on importance sampling Monte Carlo method for lattice systems / 5：
Off-lattice models / 6：
Reweighting methods / 7：
Quantum Monte Carlo methods / 8：
Monte Carlo Renormalization Group methods / 9：
Non-equilibrium and irreversible processes / 10：
Lattice gauge models: a brief introduction / 11：
A brief review of other methods of computer simulation / 12：
Monte Carlo methods outside of physics / 13：
Outlook / 14：
Introduction / 1：
Some necessary background / 2：
Simple sampling Monte Carlo methods / 3：
図書
