During the last decade each of the authors has regularly taught a graduate or senior undergraduate course in statistical mechanics. During this same period, the renormalization group approach to critical phenomena, pioneered by K. G. Wilson, greatly altered our approach to condensed matter physics. Since its introduction in the context of phase transitions, the method has found application in many other areas of physics, such as many-body theory, chaos, the conductivity of disordered materials, and fractal structures. So pervasive is its influence that we feel that it now essential that graduate students be introduced at an early stage in their career to the concepts of scaling.

Preface to the First Edition

Preface to the Second Edition

Preface to the Third 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 Magnetic Work

 1.8 Thermodynamics of Phase Transitions

 1.9 Problems

2 Statistical Ensembles

 2.1 Isolated Systems: Microcanonical Ensemble

 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 .

2.6.1 Schottky defects in a crystal

 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 A Word of Warning

 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 Symmetry Considerations

3.8.1 Potts 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 Problems

4 Applications of Mean Field Theory

 4.1 Order-Disorder Transition

 4.2 Maier-Sanpe Model

 4.3 Blume——Emery-Grifliths Model

 4.4 Mean Field Theory of Fluids: van der Waals Approach

 4.5 Spruce Budworm Model

 4.6 A Non-Equilibrium System: Two Species Asymmetric Exclusion Model

 4.7 Problems

5 Dense Gases and Liquids

 5.1Virial Expansion

 5.2 Distribution Functions

5.2.1 Pair correlation function

5.2.2 BBGKY hierarchy

5.2.3 Ornstein-Zernike equation

 5.3 Perturbation Theory

 5.4 Inhomogeneous Liquids

5.4.1 Liquid-vapor interface

5.4.2 Capillary waves

 5.5 Density-Functional Theory

5.5.1 Functional differentiation

5.5.2 Free-energy functionals and correlation functions

5.5.3 Applications

 5.6 Problems

6 Critical Phenomena I

 6.1 Ising Model in Two Dimensions

6.1.1 Transfer matrix

6.1.2 Transformation to an interacting fermion problem

6.1.3 Calculation of eigenvalues

6.1.4 Thermodynamic functions

6.1.5 Concluding remarks

 6.2 Series Expansions

6.2.1 High-temperature expansions

6.2.2 Low-temperature expansions

6.2.3 Analysis of series

 6.3 Scaling

6.3.1 Thermodynamic considerations

6.3.2 Scaling hypothesis

6.3.3 Kadanoff block spins

 6.4 Finite-Size Scaling

 6.5 Universality

 6.6 Kosterlitz-Thouless Transition

 6.7 Problems

7 Critical Phenomena II: The Renormalization Group

 7.1 The Ising Chain Revisited

 7.2 Fixed Points

 7.3 An Exactly Solvable Model: Ising Spins on a Diamond Fractal

 7.4 Position Space Renormalization: Cumulant Method

7.4.1 First-order approximation

7.4.2 Second-order approximation

 7.5 Other Position Space Renormalization Group Methods

7.5.1 Finite lattice methods

7.5.2 Adsorbed monolayers: Ising antiferromagnet

7.5.3 Monte Carlo renormalization

 7.6 Phenomen01ogical Renormalization Group

 7.7 The e-Expansion

7.7.1 The Gaussian model

7.7.2 The S4 model

7.7.3 Conclusion

 Appendix: Second Order Cumulant Expansion

 7.8 Problems

8 Stochastic Processes

 8.1 Markov Processes and the Master Equation

 8.2 Birth and Death Processes

 8.3 Branching Processes

 8.4 Fokker-Planck Equation

 8.5 Fokker-Planck Equation with Several Variables: SIR Model

 8.6 Jump Moments for Continuous Variables

8.6.1 Brownian motion

8.6.2 Rayleigh and Kramers equations

 8.7 Diffusion, First Passage and Escape

8.7.1 Natural boundaries: The Kimura-Weiss model for genetic drift

8.7.2 Artificial boundaries

8.7.3 First passage time and escape probability

8.7.4 Kramers escape rate

 8.8 Transformations of the Fokker-Planck Equation

8.8.1 Heterogeneous diffusion

8.8.2 Transformation to the SchrSdinger equation

 8.9 Problems

9 Simulations

 9.1 Molecular Dynamics

9.1.1 Conservative molecular dynamics

9.1.2 Brownian dynamics

9.1.3 Data analysis

 9.2 Monte Carlo Method

9.2.1 Discrete time Markov processes

9.2.2 Detailed balance and the Metropolis algorithm

9.2.3 Histogram methods

 9.3 Data Analysis

9.3.1 Fluctuations

9.3.2 Error estimates

9.3.3 Extrapolation to the thermodynamic limit

 9.4 The Hopfield Model of Neural Nets

 9.5 Simulated Quenching and Annealing

 9.6 Problems

10 Polymers and Membranes

 10.1 Linear Polymers

10.1.1 The freely jointed chain

10.1.2 The Gaussian chain

 10.2 Excluded Volume Effects: Flory Theory

 10.3 Polymers and the n-Vector Model

 10.4 Dense Polymer Solutions

 10.5 Membranes

10.5.1 Phantom membranes

10.5.2 Self-avoiding membranes

10.5.3 Liquid membranes

 10.6 Problems

11 Quantum Fluids

 11.1 Bose Condensation

 11.2 Superfluidity

11.2.1 Qualitative features of superfiuidity

11.2.2 Bogoliubov theory of the 4He excitation spectrum

 11.3 Superconductivity

11.3.1 Cooper problem

11.3.2 BCS ground state

11.3.3 Finite-temperature BCS theory

11.3.4 Landau-Ginzburg theory of superconductivity

 11.4 Problems

12 Linear Response Theory

 12.1 Exact Results

12.1.1 Generalized susceptibility and the structure factor

12.1.2 Thermodynamic properties

12.1.3 Sum rules and inequalities

 12.2 Mean Field Response

12.2.1 Dielectric function of the electron gas

12.2.2 Weakly interacting Bose gas

12.2.3 Excitations of the Heisenberg ferromagnet

12.2.4 Screening and plasmons

12.2.5 Exchange and correlation energy

12.2.6 Phon0ns in metals

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

12.3.1 Kubo formula

12.3.2 Entropy production and generalized currents and forces

12.3.3 Microscopic reversibility: Onsager relations

 12.4 The Boltzmann Equation

12.4.1 Fields, drift and collisions

12.4.2 DC conductivity of a metal

12.4.3 Thermal conductivity and thermoelectric effects

 12.5 Problems

13 Disordered Systems

 13.1 Single-Particle States in Disordered Systems

13.1.1 Electron states in one dimension

13.1.2 Transfer matrix

13.1.3 Localization in three dimensions

13.1.4 Density of states

 13.2 Percolation

13.2.1 Scaling theory of percolation

13.2.2 Series expansions and renormalization group

13.2.3 Rigidity percolation

13.2.4 Conclusion

 13.3 Phase Transitions in Disordered Materials

13.3.1 Statistical formalism and the replica trick

13.3.2 Nature of phase transitions

 13.4 Strongly Disordered Systems

13.4.1 Molecular glasses

13.4.2 Spin glasses

13.4.3 Sherrington-Kirkpatrick model

 13.5 Problems

A Occupation Number Representation

Bibliography

Index