平衡统计物理学 第2版 英文影印版PDF电子书下载

1 Review of Thermodynamics 1

1.1 State Variables and Equations of State 2

1.2 Laws of Thermodynamics 3

1.2.1 First law 4

1.2.2 Second law 5

1.3 Thermodynamic Potentials 10

1.4 Gibbs-Duhem and Maxwell Relations 13

1.5 Response Functions 15

1.6 Conditions for Equilibrium and Stability 17

1.7 Thermodynamics of Phase Transitions 19

1.8 Problems 23

2 Statistical Ensembles 29

2.1 Isolated Systems:MicrocanonicalEnsemble 30

2.2 Systems at Fixed Temperature:Canonical Ensemble 35

2.3 Grand Canonical Ensemble 40

2.4 Quantum Statistics 43

2.4.1 Harmonic oscillator 44

2.4.2 Noninteracting fermions 44

2.4.3 Noninteracting bosons 45

2.4.4 Density matrix 46

2.5 Maximum Entropy Principle 48

2.6 Thermodynamic Variational Principles 51

2.7 Problems 53

3 Mean Field and Landau Theory 61

3.1 Mean Field Theory of the Ising Model 63

3.2 Bragg-Williams Approximation 65

3.3 Order Disorder Transition 69

3.4 Bethe Approximation 74

3.5 Critical Behavior of Mean Field Theories 77

3.6 Ising Chain:Exact Solution 80

3.7 Landau Theory of Phase Transitions 86

3.8 Example of Symmetry Considerations:Maier-Saupe Model 89

3.9 Landau Theory of Tricritical Points 96

3.10 Landau-Ginzburg Theory for Fluctuations 103

3.11 Multicomponent Order Parameters:n-Vector Model 107

3.12 Mean Field Theory of Fluids:Van der Waals Approach 109

3.13 Problems 115

4 Dense Gases and Liquids 123

4.1 Virial Expansion 125

4.2 Distribution Functions 131

4.2.1 Pair correlation function 131

4.2.2 BBGKY hierarchy 137

4.2.3 Ornstein-Zernike equation 138

4.3 Perturbation Theory 141

4.4 Inhomogeneous Liquids 143

4.4.1 Liquid-vapor interface 143

4.4.2 Capillary waves 149

4.5 Density-Functional Theory 151

4.5.1 Functional differentiation 151

4.5.2 Free-energy functionals and correlation functions 153

4.5.3 Applications 159

4.6 Problems 161

5 Critical Phenomena Ⅰ 163

5.1 Ising Model in Two Dimensions 164

5.1.1 Transfer matrix 164

5.1.2 Transformation to an interacting fermion problem 168

5.1.3 Calculation of eigenvalues 171

5.1.4 Thermodynamic functions 174

5.1.5 Concluding remarks 179

5.2 Series Expansions 179

5.2.1 High-temperature expansions 180

5.2.2 Low-temperature expansions 186

5.2.3 Analysis of series 186

5.3 Scaling 191

5.3.1 Thermodynamic considerations 191

5.3.2 Scaling hypothesis 192

5.3.3 Kadanoff block spins 195

5.4 Finite-Size Scaling 199

5.5 Universality 204

5.6 Kosterlitz-Thouless Transition 206

5.7 Problems 214

6 Critical Phenomena Ⅱ:The Renormalization Group 217

6.1 The Ising Chain Revisited 218

6.2 Fixed Points 222

6.3 Position Space Renormalization:Cumulant Method 228

6.3.1 First-order approximation 232

6.3.2 Second-order approximation 234

6.4 Other Position Space RenormalizationGroup Methods 237

6.4.1 Finite lattice methods 237

6.4.2 Adsorbed monolayers:Ising antiferromagnet 238

6.4.3 Monte Carlo renormalization 243

6.5 Phenomenological Renormalization Group 246

6.6 The ε-Expansion 249

6.6.1 The Gaussian model 251

6.6.2 The S4 model 255

6.6.3 Critical exponents to order ε 258

6.6.4 Conclusion 264

6.7 Problems 265

7 Simulations 271

7.1 Molecular Dynamics 272

7.2 Monte Carlo Method 277

7.2.1 Markov processes 277

7.2.2 Detailed balance and the Metropolis algorithm 279

7.2.3 Histogram methods 282

7.3 Data Analysis 284

7.3.1 Fluctuations 284

7.3.2 Error estimates 286

7.3.3 Extrapolation to the thermodynamic limit 287

7.4 The Hopfield Model of Neural Nets 290

7.5 Simulated Quenching and Annealing 295

7.6 Problems 298

8 Polymers and Membranes 301

8.1 Linear Polymers 302

8.1.1 The freely jointed chain 304

8.1.2 The Gaussian chain 307

8.2 Excluded Volume Effects:Flory Theory 309

8.3 Polymers and the n-Vector Model 313

8.4 Dense Polymer Solutions 317

8.5 Membranes 323

8.5.1 Phantom membranes 324

8.5.2 Self-avoiding membranes 327

8.5.3 Liquid membranes 332

8.6 Problems 336

9 Quantum Fluids 339

9.1 Bose Condensation 339

9.2 Superfluidity 347

9.2.1 Qualitative features of superfluidity 347

9.2.2 Bogoliubov theory of the 4He excitation spectrum 356

9.3 Superconductivity 359

9.3.1 Cooper problem 360

9.3.2 BCS ground state 361

9.3.3 Finite-temperature BCS theory 365

9.3.4 Landau-Ginzburg theory of superconductivity 369

9.4 Problems 373

10 Linear Response Theory 377

10.1 Exact Results 378

10.1.1 Generalized susceptibility and the structure factor 378

10.1.2 Thermodynamic properties 385

10.1.3 Sum rules and inequalities 386

10.2 Mean Field Response 388

10.2.1 Dielectric function of the electron gas 389

10.2.2 Weakly interacting Bose gas 391

10.2.3 Excitations of the Heisenberg ferromagnet 393

10.2.4 Screening and plasmons 396

10.2.5 Exchange and correlation energy 402

10.2.6 Phonons in metals 404

10.3 Entropy Production,the Kubo Formula,and the Onsager Rela-tions for Transport Coefficients 406

10.3.1 Kubo formula 406

10.3.2 Entropy production and generalized currents and forces 408

10.3.3 Microscopic reversibility:Onsager relations 410

10.4 The Boltzmann Equation 414

10.4.1 Fields,drift and collisions 414

10.4.2 DC conductivity of a metal 417

10.4.3 Thermal conductivity and thermoelectric effects 419

10.5 Problems 423

11 Disordered Systems 429

11.1 Single-Particle States in Disordered Systems 431

11.1.1 Electron states in one dimension 432

11.1.2 Transfer matrix 433

11.1.3 Localization in three dimensions 439

11.1.4 Density of states 441

11.2 Percolation 446

11.2.1 Scaling theory of percolation 448

11.2.2 Series expansions and renormalization group 451

11.2.3 Conclusion 453

11.3 Phase Transitions in Disordered Materials 454

11.3.1 Statistical formalism and the replica trick 455

11.3.2 Nature of phase transitions 458

11.4 Strongly Disordered Systems 463

11.4.1 Molecular glasses 463

11.4.2 Spin glasses 465

11.4.3 Sherrington-Kirkpatrick model 470

11.5 Problems 476

Appendix:Occupation Number Representation 481

Bibliography 495

Index 511