这是针对从事物理、化学和材料科学的研究生和高年级本科生的专业需求编写的统计物理教材。早在1980年，作者们发现由K.G.Wilson率先将重整化群方法引入临界现象并取得成功之后，凝聚态物理的研究进入了飞速发展的黄金时代，因此认为研究生的早期教学工作应当反映这方面的动态。为此于1989年率先由Prentice-Hall出版公司出版了反映这方面特色的《平衡统计物理学》，1994年经过修订，转到World Scientific出版了本书第一版，1999年出版了第二版，现在呈现在读者面前的是2003年的版本。

　　全书共分11章，前两章分别复习热力学和统计系统理论，这部分内容既是读者学习后面各章的基础，也是为了本科期间没有接触过热力学和统计物理的学生设计的。两章都有大量习题，可以帮助读者加深理解。后面各章分别讲述平均场和朗道理论、致密气体和液体、临界现象的二维伊辛模型、级数展开、标度律、重整化群方法等。第七章介绍动力学模拟方法。八、九、十、十一各章介绍统计物理最活跃的应用领域:聚合物和薄膜、量子流体、线性响应理论、无序系统等。

Contents

Preface to the First Edition

Preface to the Second Edition

1 Review of Thermodynamics

　1.1 State Variables and Equations of State

　1.2 Laws of Thermodynamics

　1.2.1 First law

　1.2.2 Second law

　1.3 Thermodynamic Potentials

　1.4 Gibbs-Duhem and Maxwell Relations

　1.5 Response Functions

　1.6 Conditions for Equilibrium and Stability

　1.7 Thermodynamics of Phase Transitions

　1.8 Problems

2 Statistical Ensembles

　2.1 Isolated Systems: MicrocanonicalEnsemble

　2.2 Systems at Fixed Temperature: Canonical Ensemble

　2.3 Grand Canonical Ensemble

　2.4 Quantum Statistics

　2.4.1 Harmonic oscillator

　2.4.2 Noninteracting fermions

　2.4.3 Noninteracting bosons

　2.4.4 Density matrix

　2.5 Maximum Entropy Principle

　2.6 Thermodynamic Variational Principles

　2.7 Problems

3 Mean Field and Landau Theory

　3.1 Mean Field Theory of the Ising Model

　3.2 Bragg-Williams Approximation

　3.3 Order Disorder Transition

　3.4 Bethe Approximation

　3.5 Critical Behavior of Mean Field Theories

　3.6 Ising Chain: Exact Solution

　3.7 Landau Theory of Phase Transitions

　3.8 Example of Symmetry Considerations: Maier-Saupe Model

　3.9 Landau Theory of Tricritical Points

　3.10 Landau-Ginzburg Theory for Fluctuations

　3.11 Multicomponent Order Parameters: n-Vector Model

　3.12 Mean Field Theory of Fluids: Van der Waals Approach

　3.13 Problems

4 Dense Gases and Liquids

　4.1 Virial Expansion

　4.2 Distribution Functions

　　4.2.1 Pair correlation function

　　4.2.2 BBGKY hierarchy

　　4.2.3 Ornstein-Zernike equation

　4.3 Perturbation Theory

　4.4 Inhomogeneous Liquids

　　4.4.1 Liquid-vapor interface

　　4.4.2 Capillary waves

　4.5 Density-Functional Theory

　　4.5.1 Functional differentiation

　　4.5.2 Free-energy functionals and correlation functions

　　4.5.3 Applications

　4.6 Problems

5 Critical Phenomena I

　5.1 Ising Model in Two Dimensions

　　5.1.1 Transfer matrix

　　5.1.2 Transformation to an interacting fermion problem

　　5.1.3 Calculation of eigenvalues

　　5.1.4 Thermodynamic functions

　　5.1.5 Concluding remarks

　5.2 Series Expansions

　　5.2.1 High-temperature expansions

　　5.2.2 Low-temperature expansions

　　5.2.3 Analysis of series

　5.3 Scaling

　　5.3.1 Thermodynamic considerations

　　5.3.2 Scaling hypothesis

　　5.3.3 Kadanoff block spins

　5.4 Finite-Size Scaling

　5.5 Universality

　5.6 Kosterlitz-Thouless Transition

　5.7 Problems

6 Critical Phenomena II: The Renormalization Group

　6.1 The Ising Chain Revisited

　6.2 Fixed Points

　6.3 Position Space Renormalization: Cumulant Method

　　6.3.1 First-order approximation

　　6.3.2 Second-order approximation

　6.4 Other Position Space RenormalizationGroup Methods

　　6.4.1 Finite lattice methods

　　6.4.2 Adsorbed monolayers: Ising antiferromagnet

　　6.4.3 Monte Carlo renormalization

　6.5 Phenomenological Renormalization Group

　6.6 The e-Expansion

　　6.6.1 The Gaussian model

　　6.6.2 The S4 model

　　6.6.3 Critical exponents to order ε

　　6.6.4 Conclusion

　6.7 Problems

7 Simulations

　7.1 Molecular Dynamics

　7.2 Monte Carlo Method

　　7.2.1 Markov processes

　　7.2.2 Detailed balance and the Metropolis algorithm

　　7.2.3 Histogram methods

　7.3 Data Analysis

　　7.3.1 Fluctuations

　　7.3.2 Error estimates

　　7.3.3 Extrapolation to the thermodynamic limit

　7.4 The Hopfield Model of Neural Nets

　7.5 Simulated Quenching and Annealing

　7.6 Problems

8 Polymers and Membranes

　8.1 Linear Polymers

　　8.1.1 The freely jointed chain

　　8.1.2 The Gaussian chain

　8.2 Excluded Volume Effects: Flory Theory

　8.3 Polymers and the n-Vector Model

　8.4 Dense Polymer Solutions

　8.5 Membranes

　　8.5.1 Phantom membranes

　　8.5.2 Self-avoiding membranes

　　8.5.3 Liquid membranes

　8.6 Problems

9 Quantum Fluids

　9.1 Bose Condensation

　9.2 Superfluidity

　　9.2.1 Qualitative features of superfluidity

　　9.2.2 Bogoliubov theory of the aHe excitation spectrum

　9.3 Superconductivity

　　9.3.1 Cooper problem

　　9.3.2 BCS ground state

　　9.3.3 Finite-temperature BCS theory

　　9.3.4 Landau-Ginzburg theory of superconductivity

　9.4 Problems

10 Linear Response Theory

　10.1 Exact Results 378

　　10.1.1 Generalized susceptibility and the structure factor

　　10.1.2 Thermodynamic properties

　　10.1.3 Sum rules and inequalities

　10.2 Mean Field Response

　　10.2.1 Dielectric function of the electron gas

　　10.2.2 Weakly interacting Bose gas

　　10.2.3 Excitations of the Heisenberg ferromagnet

　　10.2.4 Screening and plasmons

　　10.2.5 Exchange and correlation energy

　　10.2.6 Phonons in metals

　10.3 Entropy Production, the Kubo Formula, and the Onsager Relations for Transport Coefficients

　　10.3.1 Kubo formula

　　10.3.2 Entropy production and generalized currents and forces

　　10.3.3 Microscopic reversibility: Onsager relations

　10.4 The Boltzmann Equation

　　10.4.1 Fields, drift and collisions

　　10.4.2 DC conductivity of a metal

　　10.4.3 Thermal conductivity and thermoelectric effects

　10.5 Problems

11 Disordered Systems

　11.1 Single-Particle States in Disordered Systems

　　11.1.1 Electron states in one dimension

　　11.1.2 Transfer matrix

　　11.1.3 Localization in three dimensions

　　11.1.4 Density of states

　11.2 Percolation

　　11.2.1 Scaling theory of percolation

　　11.2.2 Series expansions and renormalization group

　　11.2.3 Conclusion

　11.3 Phase Transitions in Disordered Materials

　　11.3.1 Statistical formalism and the replica trick

　　11.3.2 Nature of phase transitions

　11.4 Strongly Disordered Systems

　　11.4.1 Molecular glasses

　　11.4.2 Spin glasses

　　11.4.3 Sherrington-Kirkpatrick model

　11.5 Problems

Appendix: Occupation Number Representation

Bibliography

Index