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1.

図書

図書
Michael V. Sadovskii
出版情報: Berlin ; Boston : De Gruyter, c2019  ix, 304 p. ; 25 cm
シリーズ名: Texts and monographs in theoretical physics / edited by Michael Efroimsky, Leonard Gamberg
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2.

図書

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

図書
with contributions by K. Binder ... [et al.] ; edited by K. Binder
出版情報: Berlin ; New York : Springer-Verlag, 1979  xiii, 376 p. ; 25 cm
シリーズ名: Topics in current physics ; v. 7
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4.

図書

図書
F. Mandl
出版情報: Chichester, [West Sussex] : Wiley, c1971  xiii, 379 p. ; 23 cm
シリーズ名: The Manchester physics series
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目次情報: 続きを見る
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

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

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

図書
edited by K. Binder ; with contributions by K.Binder ... [et al.]
出版情報: Berlin ; Heidelberg ; New York ; Tokyo : Springer-Verlag, c1986  xv, 411 p. ; 25 cm
シリーズ名: Topics in current physics ; v. 7
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8.

図書

図書
editor, H.J. Raveché
出版情報: Amsterdam ; New York : North-Holland Pub. Co. , New York : sole distributors for the U.S.A. Elsevier North-Holland, c1981  xxviii, 367 p. ; 23 cm
シリーズ名: Studies in statistical mechanics / edited by J. De Boer and G.E. Uhlenbeck ; v. 9
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9.

図書

図書
R.A. Minlos
出版情報: Providence, RI : American Mathematical Society, c2000  vii, 103 p. ; 26 cm
シリーズ名: University lecture series ; v. 19
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10.

図書

図書
Jean-François Sadoc and Rémy Mosseri
出版情報: Cambridge ; New York : Cambridge University Press, 1999  xii, 307 p. ; 26 cm
シリーズ名: Collection Aléa-Saclay : monographs and texts in statistical physics
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目次情報: 続きを見る
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

図書
edited by Massimo Picardello, Wolfgang Woess
出版情報: Cambridge : Cambridge University Press, 1999  viii, 361 p. ; 24 cm
シリーズ名: Symposia mathematica ; v. 39
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12.

図書

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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目次情報: 続きを見る
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

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

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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目次情報: 続きを見る
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

図書
V.A. Malyshev, R.A. Minlos
出版情報: Providence, R.I. : American Mathematical Society, c1995  viii, 298 p. ; 27 cm
シリーズ名: Translations of mathematical monographs ; v. 143
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目次情報: 続きを見る
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

図書
by E.M. Lifshitz and L.P. Pitaevskiĭ ; translated from the Russian by J.B. Sykes and M.J. Kearsley
出版情報: Oxford : Butterworth-Heinemann, 1995, c1980  x, 387 p. ; 25 cm
シリーズ名: Course of theoretical physics ; v. 9 . Statistical physics / L.D. Landau and E. M. Lifshitz ; pt. 2
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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
17.

図書

図書
by Y.M. Berezansky and Y.G. Kondratiev
出版情報: Dordrecht ; Boston : Kluwer Academic, c1995  2 v. ; 25 cm
シリーズ名: Mathematical physics and applied mathematics ; v. 12
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18.

図書

図書
Hagen Kleinert
出版情報: Singapore : World Scientific, c1995  xxvii, 891 p. ; 23 cm
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19.

図書

図書
出版情報: Malabar, Fla. : R.E. Krieger, 1986  xx, 520 p. ; 28 cm
シリーズ名: Statistical and thermal physics / by Shigeji Fujita ; pt. 1
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20.

図書

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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目次情報: 続きを見る
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

図書
R. Kubo, M. Toda, N. Hashitsume
出版情報: Berlin : Springer-Verlag, c1985  xvi, 279 p. ; 24 cm
シリーズ名: Springer series in solid-state sciences ; 31 . Statistical physics ; 2
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22.

雑誌

雑誌
出版情報: Berlin : Springer
巻次年月次: Vol. 20 (1975)-v. 37, no. 4 (1980)
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23.

図書

図書
Ilya Prigogine, Robert Herman
出版情報: New York : American Elsevier, 1971  xix, 100 p. ; 22 cm
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24.

図書

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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25.

図書

図書
edited by K. Binder ; with contributions by A. Baumgärtner ... [et al.]
出版情報: Berlin ; Tokyo : Springer-Verlag, c1992  xvi, 392 p. ; 25 cm
シリーズ名: Topics in applied physics ; v. 71
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26.

図書

図書
edited by Eric Goles and Servet Martínez
出版情報: Dordrecht ; Boston : Kluwer Academic Publishers, c1992  x, 207 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 75
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27.

図書

図書
Roger Balian ; translated by D. ter Haar and J.F. Gregg
出版情報: Berlin ; Tokyo : Springer-Verlag, c1991-1992  2 v. ; 25 cm
シリーズ名: Texts and monographs in physics
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28.

図書

図書
Boris Nahapetian
出版情報: Stuttgart : Teubner, 1991  244 p. ; 21 cm
シリーズ名: Teubner-Texte zur Mathematik ; Bd. 123
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29.

図書

図書
Rick Durrett, Harry Kesten, editors
出版情報: Boston : Birkhäuser, 1991  ix, 455 p. ; 24 cm
シリーズ名: Progress in probability ; 28
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30.

図書

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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目次情報: 続きを見る
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)
31.

図書

図書
Neal Madras, Gordon Slade
出版情報: Boston : Birkhäuser, c1993  xiv, 425 p. ; 25 cm
シリーズ名: Probability and its applications
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32.

図書

図書
[by] Don C. Kelly
出版情報: New York : Academic Press, [1973]  xiii, 421 p. ; 24 cm
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33.

図書

図書
M. Toda, R. Kubo, N. Saitô
出版情報: Berlin ; Tokyo : Springer-Verlag, c1992  xvi, 252 p. ; 24 cm
シリーズ名: Springer series in solid-state sciences ; 30 . Statistical physics ; 1
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34.

図書

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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35.

図書

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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36.

図書

図書
A. Ranfagni ... [et al]
出版情報: Singapore ; Teaneck, N.J. : World Scientific, c1990  xi, 226 p. ; 24 cm
シリーズ名: World Scientific lecture notes in physics ; v. 36
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37.

図書

図書
Claude Itzykson, Jean-Michel Drouffe
出版情報: Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1989  xvi, 403 p. ; 24 cm
シリーズ名: Cambridge monographs on mathematical physics ; . Statistical field theory / Claude Itzykson, Jean-Michel Drouffe ; v. 1
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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:
38.

図書

図書
by N.N. Bogolyubov, Jr. ; Translated and edited by P.J. Shepherd
出版情報: Oxford ; New York : Pergamon Press, 1972  x, 170 p. ; 22 cm
シリーズ名: International series of monographs in natural philosophy ; v. 43
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39.

図書

図書
Hagen Kleinert
出版情報: Singapore ; Teaneck, N.J. : World Scientific, c1990  xxi, 664 p. ; 23 cm
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40.

図書

図書
M. Toda, R. Kubo, N. Saitō
出版情報: Berlin ; New York : Springer-Verlag, 1983  xvi, 249 p. ; 24 cm
シリーズ名: Springer series in solid-state sciences ; 30 . Statistical physics ; v. 1
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41.

図書

図書
C. Kittel
出版情報: New York : Wiley, c1958 , London : Chapman & Hall  ix, 228 p. ; 24 cm
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42.

図書

図書
by L. D. Landau and E. M. Lifshitz ; translated from the Russian by E. Peierls and R. F. Peierls
出版情報: London : Pergamon Press, 1958  x, 484 p. ; 25 cm
シリーズ名: Course of theoretical physics ; vol. 5
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43.

図書

図書
Gregory H. Wannier
出版情報: New York : Dover Publications, 1987, c1966  xii, 532 p. ; 22 cm
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44.

図書

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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45.

図書

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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46.

図書

図書
D.J.A. Welsh
出版情報: Cambridge : Cambridge University Press, 1993  viii, 163 p. ; 23 cm
シリーズ名: London Mathematical Society lecture note series ; 186
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目次情報: 続きを見る
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:
47.

図書

図書
Setsuo Ichimaru
出版情報: Reading, Mass. : Addison-Wesley, c1994  xiv, 289 p. ; 24 cm
シリーズ名: Frontiers in physics ; v. 88 . Statistical plasma physics ; v. 2
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48.

図書

図書
Josef Honerkamp
出版情報: Berlin : Springer, c2002  xiv, 515 p. ; 24 cm
シリーズ名: Advanced texts in physics
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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:
49.

図書

図書
Klaus R. Mecke, Dietrich Stoyan (eds.)
出版情報: Berlin : Springer, c2000  xii, 415 p. ; 25 cm
シリーズ名: Lecture notes in physics ; 554
Physics and astronomy online library
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目次情報: 続きを見る
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
50.

図書

図書
Nandita Rudra, P. Rudra
出版情報: Hackensack : World Scientific, c2010  xvii, 229 p. ; 24 cm
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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 4He / 9.6.1:
Landau's 2-Fluid Model / 9.6.2:
Systematics of Liquid 3He / 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:
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