平衡态统计物理学 英文版 影印本PDF电子书下载

1 Review of Thermodynamics 1

1.1 State Variables and Equations of State 1

1.2 Laws of Thermodynamics 3

1.2.1 First law 3

1.2.2 Second law 5

1.3 Thermodynamic Potentials 9

1.4 Gibbs-Duhem and Maxwell Relations 12

1.5 Response Functions 14

1.6 Conditions for Equilibrium and Stability 16

1.7 Magnetic Work 18

1.8 Thermodynamics of Phase Transitions 20

1.9 Problems 24

2 Statistical Ensembles 29

2.1 Isolated Systems:Microcanonical Ensemble 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 53

2.6.1 Schottky defects in a crystal 53

2.7 Problems 54

3 Mean Field and Landau Theory 63

3.1 Mean Field Theory of the Ising Model 64

3.2 Bragg-Williams Approximation 67

3.3 A Word of Warning 69

3.4 Bethe Approximation 71

3.5 Critical Behavior of Mean Field Theories 74

3.6 Ising Chain:Exact Solution 77

3.7 Landau Theory of Phase Transitions 83

3.8 Symmetry Considerations 86

3.8.1 Potts model 87

3.9 Landau Theory of Tricritical Points 90

3.10 Landau-Ginzburg Theory for Fluctuations 94

3.11 Multicomponent Order Parameters:n-Vector Model 98

3.12 Problems 100

4 Applications of Mean Field Theory 109

4.1 Order-Disorder Transition 110

4.2 Maier-Saupe Model 114

4.3 Blume-Emery-Griffiths Model 120

4.4 Mean Field Theory of Fluids:van der Waals Approach 123

4.5 Spruce Budworm Model 129

4.6 A Non-Equilibrium System:Two Species Asymmetric Exclusion Model 132

4.7 Problems 137

5 Dense Gases and Liquids 143

5.1 Virial Expansion 145

5.2 Distribution Functions 151

5.2.1 Pair correlation function 151

5.2.2 BBGKY hierarchy 157

5.2.3 Ornstein-Zernike equation 158

5.3 Perturbation Theory 161

5.4 Inhomogeneous Liquids 163

5.4.1 Liquid-vapor interface 164

5.4.2 Capillary waves 169

5.5 Density-Functional Theory 171

5.5.1 Functional differentiation 171

5.5.2 Free-energy functionals and correlation functions 174

5.5.3 Applications 179

5.6 Problems 181

6 Critical Phenomena Ⅰ 183

6.1 Ising Model in Two Dimensions 184

6.1.1 Transfer matrix 184

6.1.2 Transformation to an interacting fermion problem 188

6.1.3 Calculation of eigenvalues 191

6.1.4 Thermodynamic functions 194

6.1.5 Concluding remarks 199

6.2 Series Expansions 199

6.2.1 High-temperature expansions 200

6.2.2 Low-temperature expansions 206

6.2.3 Analysis of series 206

6.3 Scaling 211

6.3.1 Thermodynamic considerations 211

6.3.2 Scaling hypothesis 212

6.3.3 Kadanoff block spins 215

6.4 Finite-Size Scaling 218

6.5 Universality 223

6.6 Kosterlitz-Thouless Transition 226

6.7 Problems 233

7 Critical Phenomena Ⅱ:The Renormalization Group 237

7.1 The Ising Chain Revisited 238

7.2 Fixed Points 242

7.3 An Exactly Solvable Model:Ising Spins on a Diamond Fractal 248

7.4 Position Space Renormalization:Cumulant Method 258

7.4.1 First-order approximation 262

7.4.2 Second-order approximation 264

7.5 Other Position Space Renormalization Group Methods 267

7.5.1 Finite lattice methods 267

7.5.2 Adsorbed monolayers:Ising antiferromagnet 268

7.5.3 Monte Carlo renormalization 272

7.6 Phenomeno1ogical Renormalization Group 275

7.7 The ε-Expansion 279

7.7.1 The Gaussian model 281

7.7.2 The S4 model 284

7.7.3 Conclusion 290

Appendix:Second Order Cumulant Expansion 292

7.8 Problems 295

8 Stochastic Processes 303

8.1 Markov Processes and the Master Equation 304

8.2 Birth and Death Processes 306

8.3 Branching Processes 309

8.4 Fokker-Planck Equation 313

8.5 Fokker-Planck Equation with Several Variables:SIR Model 316

8.6 Jump Moments for Continuous Variables 321

8.6.1 Brownian motion 323

8.6.2 Rayleigh and Kramers equations 326

8.7 Diffusion,First Passage and Escape 328

8.7.1 Natural boundaries:The Kimura-Weiss model for genetic drift 329

8.7.2 Artificial boundaries 331

8.7.3 First passage time and escape probability 332

8.7.4 Kramers escape rate 337

8.8 Transformations of the Fokker-Planck Equation 340

8.8.1 Heterogeneous diffusion 340

8.8.2 Transformation to the Schr？dinger equation 343

8.9 Problems 345

9 Simulations 349

9.1 Molecular Dynamics 350

9.1.1 Conservative molecular dynamics 351

9.1.2 Brownian dynamics 353

9.1.3 Data analysis 355

9.2 Monte Carlo Method 357

9.2.1 Discrete time Markov processes 358

9.2.2 Detailed balance and the Metropolis algorithm 359

9.2.3 Histogram methods 363

9.3 Data Analysis 365

9.3.1 Fluctuations 365

9.3.2 Error estimates 367

9.3.3 Extrapolation to the thermodynamic limit 368

9.4 The Hopfield Model of Neural Nets 371

9.5 Simulated Quenching and Annealing 376

9.6 Problems 379

10 Polymers and Membranes 383

10.1 Linear Polymers 384

10.1.1 The freely jointed chain 386

10.1.2 The Gaussian chain 389

10.2 Excluded Volume Effects:Flory Theory 391

10.3 Polymers and the n-Vector Model 395

10.4 Dense Polymer Solutions 400

10.5 Membranes 405

10.5.1 Phantom membranes 406

10.5.2 Self-avoiding membranes 409

10.5.3 Liquid membranes 415

10.6 Problems 418

11 Quantum Fluids 421

11.1 Bose Condensation 422

11.2 Superfluidity 430

11.2.1 Qualitative features of superfluidity 430

11.2.2 Bogoliubov theory of the 4He excitation spectrum 439

11.3 Superconductivity 442

11.3.1 Cooper problem 443

11.3.2 BCS ground state 445

11.3.3 Finite-temperature BCS theory 449

11.3.4 Landau-Ginzburg theory of superconductivity 453

11.4 Problems 456

12 Linear Response Theory 461

12.1 Exact Results 462

12.1.1 Generalized susceptibility and the structure factor 462

12.1.2 Thermodynamic properties 469

12.1.3 Sum rules and inequalities 470

12.2 Mean Field Response 472

12.2.1 Dielectric function of the electron gas 473

12.2.2 Weakly interacting Bose gas 475

12.2.3 Excitations of the Heisenberg ferromagnet 477

12.2.4 Screening and plasmons 480

12.2.5 Exchange and correlation energy 486

12.2.6 Phonons in metals 487

12.3 Entropy Production,the Kubo Formula,and the Onsager Rela-tions for Transport Coefficients 490

12.3.1 Kubo formula 490

12.3.2 Entropy production and generalized currents and forces 492

12.3.3 Microscopic reversibility:Onsager relations 494

12.4 The Boltzmann Equation 498

12.4.1 Fields,drift and collisions 498

12.4.2 DC conductivity of a metal 500

12.4.3 Thermal conductivity and thermoelectric effects 503

12.5 Problems 507

13 Disordered Systems 513

13.1 Single-Particle States in Disordered Systems 515

13.1.1 Electron states in one dimension 516

13.1.2 Transfer matrix 517

13.1.3 Localization in three dimensions 523

13.1.4 Density of states 525

13.2 Percolation 530

13.2.1 Scaling theory of percolation 533

13.2.2 Series expansions and renormalization group 536

13.2.3 Rigidity percolation 540

13.2.4 Conclusion 542

13.3 Phase Transitions in Disordered Materials 542

13.3.1 Statistical formalism and the replica trick 544

13.3.2 Nature of phase transitions 546

13.4 Strongly Disordered Systems 551

13.4.1 Molecular glasses 552

13.4.2 Spin glasses 554

13.4.3 Sherrington-Kirkpatrick model 558

13.5 Problems 565

A Occupation Number Representation 569

Bibliography 583

Index 603