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
