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
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