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図書
図書
1. Conformal invariance and critical phenomena
Malte Henkel
出版情報: Berlin ; Tokyo : Springer, c1999  xvii, 417 p. ; 25 cm
シリーズ名: Texts and monographs in physics
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目次情報: 続きを見る
Critical Phenomena: a Reminder / 1：
Phase Diagrams and Critical Exponents / 1.1：
Scale Invariance and Scaling Relations / 1.2：
Some Simple Spin Systems / 1.3：
Ising Model / 1.3.1：
Tricritical Ising Model / 1.3.2：
q-States Potts Model / 1.3.3：
Vector Potts Model / 1.3.4：
XY Model / 1.3.5：
Yang-Lee Edge Singularity / 1.3.6：
Percolation / 1.3.7：
Linear Polymers / 1.3.8：
Restricted Solid-On-Solid Models / 1.3.9：
Some Experimental Examples / 1.4：
Correspondence Between Statistical Systems and Field Theory / 1.5：
Correspondence of Physical Quantities / 1.6：
Free Energy Density / 1.6.1：
Correlation Functions / 1.6.2：
Correlation Lengths / 1.6.3：
Conformal Invariance / 2：
From Scale Invariance to Conformal Invariance / 2.1：
Conformal Transformations in d Dimensions / 2.2：
Conformal Transformations in Two Dimensions / 2.3：
Conformal Invariance in Two Dimensions / 2.4：
Correlation Functions of Quasi-primary Operators / 2.5：
The Energy-Momentum Tensor / 2.6：
Finite-Size Scaling / 3：
Statistical Systems in Finite Geometries / 3.1：
Finite-Size Scaling Hypothesis / 3.2：
Universality / 3.3：
Phenomenological Renormalization / 3.4：
Consequences of Conformal Invariance / 3.5：
Comparison with Experiments / 3.6：
Representation Theory of the Virasoro Algebra / 4：
Verma Module / 4.1：
Hilbert Space Structure / 4.2：
Null Vectors / 4.3：
Kac Formula and Unitarity / 4.4：
Minimal Characters / 4.5：
Correlators, Null Vectors and Operator Algebra / 5：
Null Vectors and Correlation Functions / 5.1：
Operator Algebra and Associativity / 5.2：
Analyticity and the Monodromy Problem / 5.3：
Riemann's Method / 5.4：
Ising Model Correlators / 6：
Spin-Density Four-Point Function / 6.1：
Energy-Density Four-Point Function / 6.2：
Mixed Four-Point Functions / 6.3：
Semi-Local Four-Point Functions / 6.4：
Coulomb Gas Realization / 7：
The Free Bosonic Scalar Field / 7.1：
Screened Coulomb Gas / 7.2：
Minimal Correlation Functions / 7.3：
Minimal Algebras and OPE Coefficients / 7.4：
The Hamiltonian Limit and Universality / 8：
Hamiltonian Limit in the Ising Model / 8.1：
Hubbard-Stratonovich Transformation / 8.2：
Hamiltonian Spectrum and Conformal Invariance / 8.3：
Temperley-Lieb Algebra / 8.5：
Laudau-Ginzburg Classification / 8.6：
Numerical Techniques / 9：
Simple Properties of Quantum Hamiltonians / 9.1：
Some Further Physical Quantities and their Critical Exponents / 9.2：
Translation Invariance / 9.3：
Diagonalization / 9.4：
Extrapolation / 9.5：
VBS Algorithm / 9.5.1：
BST Algorithm / 9.5.2：
The DMRG Algorithm / 9.6：
Conformal Invariance in the Ising Quantum Chain / 10：
Exact Diagonalization / 10.1：
General Remarks / 10.1.1：
Jordan-Wigner Transformation / 10.1.2：
Diagonalization of a Quadratic Form / 10.1.3：
Eigenvalue Spectrum and Normalization / 10.1.4：
Character Functions
Finite-Size Scaling Analysis / 10.2：
Ground State Energy / 10.3.1：
Operator Content / 10.3.2：
Finite-Size Corrections / 10.3.3：
Finite-Size Scaling Functions / 10.3.4：
The Spin I Quantum Chain / 10.3：
The Virasoro Generators / 10.4：
Recapitulation / 10.5：
Modular Invariance / 11：
The Modular Group / 11.1：
Implementation for Minimal Models / 11.2：
Modular Invariance at c =1 / 11.3：
Circle or Coulomb Models / 11.3.1：
Orbifold Models / 11.3.2：
Lattice Realizations / 11.4：
Further Developments and Applications / 12：
Three-States Potts Model / 12.1：
Supersymmetry and Superconformal Invariance / 12.2：
Ashkin Teller Model / 12.3：
Relation with the XXZ Quantum Chain / 12.4.1：
Global Symmetry and Boundary Conditions / 12.4.2：
Phase Diagram / 12.4.3：
Operator Content on the c =1 Line / 12.4.4：
XXZ Quantum Chain / 12.5：
Ising Correlation Functions on Cylinders / 12.7：
Alternative Realizations of the Conformal Algebra / 12.8：
Logarithmic Conformal Theories / 12.8.1：
Lattice Two-Point Functions / 12.8.2：
Polymers / 12.9：
Lattice Animals / 12.10.1：
A Sketch of Conformal Turbulence / 12.11：
Some Remarks on 3D Systems / 12.12：
Conformal Perturbation Theory / 13：
Correlation Functions in the Strip Geometry / 13.1：
General Remarks on Corrections to the Critical Behaviour / 13.2：
Tower of the Identity / 13.3：
Application to the Ising Model / 13.3.2：
Application to the Three-States Potts Model / 13.3.3：
Checking the Operator Content from Finite-Size Corrections / 13.3.4：
Ising Model: Thermal Perturbation / 13.4：
Ising Model: Magnetic Perturbation / 13.4.2：
Truncation Method / 13.5：
The Vicinity of the Critical Point / 14：
The c-Theorem / 14.1：
Application to Polymers / 14.1.1：
Conserved Currents Close to Criticality / 14.2：
Exact S-Matrix Approach / 14.3：
Phenomenological Consequences / 14.4：
Integrable Perturbations / 14.4.1：
Universal Critical Amplitude Ratios / 14.4.2：
Chiral Potts Model / 14.4.3：
Oriented Interacting Polymers / 14.4.4：
Non-integrable Perturbations / 14.4.5：
Asymptotic Finite-Size Scaling Functions / 14.5：
Surface Critical Phenomena / 15：
Systems with a Boundary / 15.1：
Conformal Invariance Close to a Free Surface / 15.2：
Finite-Size Scaling with Free Boundary Conditions / 15.3：
Surface Operator Content / 15.4：
Temperley-Lieb Algebra and Relation with the XXZ Chain / 15.4.1：
Ashkin-Teller Model / 15.4.4：
Profiles / 15.4.7：
Defect Lines
Aperiodically Modulated Systems / 15.6.1：
Persistent Currents in Small Rings / 15.6.2：
Strongly Anisotropic Scaling / 16：
Dynamical Scaling / 16.1：
Schrödinger Invariance / 16.2：
Towards Local Scale Invariance for General ? / 16.3：
Some Remarks on Reaction-Diffusion Processes / 16.4：
Anhang/Annexe
List of Tables
List of Figures
References
Index
Critical Phenomena: a Reminder / 1：
Phase Diagrams and Critical Exponents / 1.1：
Scale Invariance and Scaling Relations / 1.2：
2.

図書
図書
2. Ageing and dynamical scaling far from equilibrium (: hbk.)
Malte Henkel, Michel Pleimling
出版情報: Dordrecht : Springer, c2010  xxi, 544 p. ; 24 cm
シリーズ名: Theoretical and mathematical physics ; . Non-equilibrium phase transitions ; v. 2
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3.

図書
図書
3. Absorbing phase transitions (: hbk.)
Malte Henkel, Haye Hinrichsen, Sven Lübeck
出版情報: Dordrecht : Springer , Bristol : In association with Canopus Academic Publishing Limited, c2008  xi, 385 p. ; 24 cm
シリーズ名: Theoretical and mathematical physics ; . Non-equilibrium phase transitions ; v. 1
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目次情報: 続きを見る
Introduction / 1：
Problems
Survey of Equilibrium Critical Phenomena / 2：
Phase Transitions in Equilibrium Systems / 2.1：
Notations / 2.1.1：
Phase Transitions in Ferromagnetic Systems / 2.1.2：
Power-law Scaling / 2.1.3：
Scale-Invariance and Universality / 2.2：
Scale-Invariance / 2.2.1：
Scaling Functions and Data Collapses / 2.2.2：
Universality Classes / 2.2.3：
Experimental Evidence of Universality / 2.2.4：
Mean-Field and Renormalisation Group Methods / 2.3：
Mean-Field Theory of Ferromagnetic Systems / 2.3.1：
Universal Amplitude Ratios / 2.3.2：
Remarks on Renormalisation-Group Theory / 2.3.3：
Scaling Laws Induced by Renormalisation-Group Theory / 2.3.4：
Field-Theory and ?-Expansion / 2.3.5：
Surface Critical Phenomena / 2.3.6：
Finite-Size Scaling / 2.3.7：
Fluctuation-Dissipation Theorem / 2.4：
From Scale-Invariance to Conformal Invariance / 2.5：
Directed Percolation / 3：
Directed Percolation at First Glance / 3.1：
Directed Percolation as a Stochastic Process / 3.2：
Basic Scaling Behaviour / 3.2.1：
Universality and the DP Conjecture / 3.2.2：
Simple Mean-Field Approximation / 3.2.3：
Phenomenological Langevin Equation / 3.2.4：
Update Schemes and Evolution Equations / 3.2.5：
Lattice Models of Directed Percolation / 3.3：
Domany-Kinzel Automaton / 3.3.1：
Contact Process / 3.3.2：
Pair-Contact Process / 3.3.3：
Threshold Transfer Process / 3.3.4：
Ziff-Gulari-Barshad Model / 3.3.5：
Further Non-equilibrium Phenomena Related to DP / 3.3.6：
Experiments Related to Directed Percolation / 3.4：
Experiments Resembling DP Dynamics / 3.4.1：
Growth Processes Related to DP / 3.4.2：
Intermittent Turbulence / 3.4.3：
Discussion / 3.4.4：
Scaling Properties of Absorbing Phase Transitions / 4：
Scaling in the Steady-State / 4.1：
Order Parameters / 4.1.1：
Rapidity-Reversal Symmetry of Directed Percolation / 4.1.2：
Two-Point Correlation Function in the Steady-State / 4.1.3：
Empty-Interval Probabilities in the Steady-State / 4.1.6：
The External Field h / 4.1.7：
Fluctuations of the Order-Parameter in the Steady-State / 4.1.8：
Finite-Size Scaling in the Steady-State / 4.1.9：
Dynamical Scaling Behaviour / 4.2：
Homogeneously Active Initial State / 4.2.1：
Pair-Connectedness Function, I / 4.2.2：
Spreading Profile at Criticality / 4.2.3：
Clusters Generated from a Single Seed / 4.2.4：
Properties of Clusters in the Absorbing Phase / 4.2.5：
Pair-Connectedness Function, II / 4.2.6：
Response Function / 4.2.7：
Early-Time Behaviour and Critical Initial Slip / 4.2.8：
Fractal Initial Conditions / 4.2.9：
Influence of an External Field / 4.2.10：
Universality of Finite-Size Amplitudes / 4.2.11：
Methods of Analysis / 4.3：
Exact Diagonalisation / 4.3.1：
Yang-Lee and Fisher Zeros / 4.3.2：
Series Expansion / 4.3.3：
Field-Theoretical Methods / 4.3.4：
Methods for Exact Solution / 4.3.5：
Monte Carlo Simulations / 4.3.6：
Universal Moment Ratios / 4.3.7：
Density-Matrix Renormalisation-Group Methods / 4.3.8：
Other Critical Properties / 4.4：
Surface Critical Behaviour / 4.4.1：
Persistence Exponents / 4.4.2：
Universality Classes Different from Directed Percolation / 5：
Parity-Conserving Universality Class / 5.1：
Voter Universality Class / 5.2：
The Classical Voter Model / 5.2.1：
Voter-Type Phase Transitions / 5.2.2：
Compact Directed Percolation / 5.3：
Tricritical Directed Percolation / 5.4：
Mean-Field Approximation of TDP / 5.4.1：
Numerical Simulations of TDP / 5.4.2：
Dynamical Percolation / 5.5：
Long-Range Interactions / 5.6：
DP with Spatial Lévy Flights / 5.6.1：
DP with Temporal Long-Range Interactions / 5.6.2：
Other Models with Long-Range Interactions by Levy Flights / 5.6.3：
Simulating Models with Long-Range Interactions / 5.6.4：
Manna Universality Class / 5.7：
Manna Model / 5.7.1：
Conserved Threshold Transfer Process (CTTP) / 5.7.2：
Conserved Lattice Gas (CLG) and Other Reaction-Diffusion Processes / 5.7.3：
Scaling Properties / 5.7.4：
Relationship Between Absorbing Phase Transitions and Self-Organised Criticality (SOC) / 5.7.5：
Absorbing Phase Transitions and SOC: Mean-Field Approximation / 5.7.6：
Relating Critical Exponents of SOC and Absorbing Phase Transitions / 5.7.7：
Pair-Contact Process with Diffusion / 5.8：
First-Order Phase Transitions / 5.9：
Stabilisation by Elimination of Minority Islands / 5.9.1：
First-Order Transitions in One Spatial Dimension / 5.9.2：
Impossibility of Discontinuous Phase Transitions in Fluctuating One-Dimensional Systems / 5.9.3：
Phase Coexistence and Hysteresis Cycles / 5.9.4：
Crossover Phenomena / 5.10：
Crossover from DP to TDP / 5.10.1：
Crossover from DP to CDP / 5.10.2：
Crossover to Mean-Field Scaling Behaviour / 5.10.3：
Quenched Disorder / 5.11：
Temporally Quenched Disorder / 5.11.1：
Spatially Quenched Disorder / 5.11.2：
Attempts of Classification / 5.12：
Some Open Questions / 5.13：
Appendices
Equilibrium Models / A：
Potts Model / A.1：
Clock Model / A.2：
Turban Model / A.3：
Baxter-Wu Model / A.4：
Blume-Capel Model / A.5：
XY Model / A.6：
O(n) Model / A.7：
Double Exchange Model / A.8：
Frustrated Spin Models / A.9：
Hilhorst-van Leeuven Model / A.10：
Scaling Laws for Absorbing Phase Transitions / B：
Diagonalisation of Time-Evolution Operators / C：
Langevin Equations and Path Integrals / D：
Mean-Field Approximations / E：
Simple Mean-Field/Site Approximation / E.1：
Pair-Approximation / E.2：
The 'Hop-Away' Mean-Field Approximation / E.3：
Finite-Size Scaling Techniques / F：
Sequences of Finite-Size Estimates / F.1：
Sequence Extrapolation / F.2：
Numerical Methods / G：
Simulational Techniques / G.1：
Computation of Response Functions / G.2：
Fractal Dimensions / H：
Solutions
Frequently Used Symbols
Abbreviations
References
List of tables
List of figures
Index
Introduction / 1：
Problems
Survey of Equilibrium Critical Phenomena / 2：
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