平衡态统计物理学 英文版 影印本PDF|Epub|txt|kindle电子书版本网盘下载

平衡态统计物理学 英文版 影印本PDF格式电子书版下载

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1 Review of Thermodynamics1

1.1 State Variables and Equations of State1

1.2 Laws of Thermodynamics3

1.2.1 First law3

1.2.2 Second law5

1.3 Thermodynamic Potentials9

1.4 Gibbs-Duhem and Maxwell Relations12

1.5 Response Functions14

1.6 Conditions for Equilibrium and Stability16

1.7 Magnetic Work18

1.8 Thermodynamics of Phase Transitions20

1.9 Problems24

2 Statistical Ensembles29

2.1 Isolated Systems:Microcanonical Ensemble30

2.2 Systems at Fixed Temperature:Canonical Ensemble35

2.3 Grand Canonical Ensemble40

2.4 Quantum Statistics43

2.4.1 Harmonic oscillator44

2.4.2 Noninteracting fermions44

2.4.3 Noninteracting bosons45

2.4.4 Density matrix46

2.5 Maximum Entropy Principle48

2.6 Thermodynamic Variational Principles53

2.6.1 Schottky defects in a crystal53

2.7 Problems54

3 Mean Field and Landau Theory63

3.1 Mean Field Theory of the Ising Model64

3.2 Bragg-Williams Approximation67

3.3 A Word of Warning69

3.4 Bethe Approximation71

3.5 Critical Behavior of Mean Field Theories74

3.6 Ising Chain:Exact Solution77

3.7 Landau Theory of Phase Transitions83

3.8 Symmetry Considerations86

3.8.1 Potts model87

3.9 Landau Theory of Tricritical Points90

3.10 Landau-Ginzburg Theory for Fluctuations94

3.11 Multicomponent Order Parameters:n-Vector Model98

3.12 Problems100

4 Applications of Mean Field Theory109

4.1 Order-Disorder Transition110

4.2 Maier-Saupe Model114

4.3 Blume-Emery-Griffiths Model120

4.4 Mean Field Theory of Fluids:van der Waals Approach123

4.5 Spruce Budworm Model129

4.6 A Non-Equilibrium System:Two Species Asymmetric Exclusion Model132

4.7 Problems137

5 Dense Gases and Liquids143

5.1 Virial Expansion145

5.2 Distribution Functions151

5.2.1 Pair correlation function151

5.2.2 BBGKY hierarchy157

5.2.3 Ornstein-Zernike equation158

5.3 Perturbation Theory161

5.4 Inhomogeneous Liquids163

5.4.1 Liquid-vapor interface164

5.4.2 Capillary waves169

5.5 Density-Functional Theory171

5.5.1 Functional differentiation171

5.5.2 Free-energy functionals and correlation functions174

5.5.3 Applications179

5.6 Problems181

6 Critical Phenomena Ⅰ183

6.1 Ising Model in Two Dimensions184

6.1.1 Transfer matrix184

6.1.2 Transformation to an interacting fermion problem188

6.1.3 Calculation of eigenvalues191

6.1.4 Thermodynamic functions194

6.1.5 Concluding remarks199

6.2 Series Expansions199

6.2.1 High-temperature expansions200

6.2.2 Low-temperature expansions206

6.2.3 Analysis of series206

6.3 Scaling211

6.3.1 Thermodynamic considerations211

6.3.2 Scaling hypothesis212

6.3.3 Kadanoff block spins215

6.4 Finite-Size Scaling218

6.5 Universality223

6.6 Kosterlitz-Thouless Transition226

6.7 Problems233

7 Critical Phenomena Ⅱ:The Renormalization Group237

7.1 The Ising Chain Revisited238

7.2 Fixed Points242

7.3 An Exactly Solvable Model:Ising Spins on a Diamond Fractal248

7.4 Position Space Renormalization:Cumulant Method258

7.4.1 First-order approximation262

7.4.2 Second-order approximation264

7.5 Other Position Space Renormalization Group Methods267

7.5.1 Finite lattice methods267

7.5.2 Adsorbed monolayers:Ising antiferromagnet268

7.5.3 Monte Carlo renormalization272

7.6 Phenomeno1ogical Renormalization Group275

7.7 The ε-Expansion279

7.7.1 The Gaussian model281

7.7.2 The S4 model284

7.7.3 Conclusion290

Appendix:Second Order Cumulant Expansion292

7.8 Problems295

8 Stochastic Processes303

8.1 Markov Processes and the Master Equation304

8.2 Birth and Death Processes306

8.3 Branching Processes309

8.4 Fokker-Planck Equation313

8.5 Fokker-Planck Equation with Several Variables:SIR Model316

8.6 Jump Moments for Continuous Variables321

8.6.1 Brownian motion323

8.6.2 Rayleigh and Kramers equations326

8.7 Diffusion,First Passage and Escape328

8.7.1 Natural boundaries:The Kimura-Weiss model for genetic drift329

8.7.2 Artificial boundaries331

8.7.3 First passage time and escape probability332

8.7.4 Kramers escape rate337

8.8 Transformations of the Fokker-Planck Equation340

8.8.1 Heterogeneous diffusion340

8.8.2 Transformation to the Schr？dinger equation343

8.9 Problems345

9 Simulations349

9.1 Molecular Dynamics350

9.1.1 Conservative molecular dynamics351

9.1.2 Brownian dynamics353

9.1.3 Data analysis355

9.2 Monte Carlo Method357

9.2.1 Discrete time Markov processes358

9.2.2 Detailed balance and the Metropolis algorithm359

9.2.3 Histogram methods363

9.3 Data Analysis365

9.3.1 Fluctuations365

9.3.2 Error estimates367

9.3.3 Extrapolation to the thermodynamic limit368

9.4 The Hopfield Model of Neural Nets371

9.5 Simulated Quenching and Annealing376

9.6 Problems379

10 Polymers and Membranes383

10.1 Linear Polymers384

10.1.1 The freely jointed chain386

10.1.2 The Gaussian chain389

10.2 Excluded Volume Effects:Flory Theory391

10.3 Polymers and the n-Vector Model395

10.4 Dense Polymer Solutions400

10.5 Membranes405

10.5.1 Phantom membranes406

10.5.2 Self-avoiding membranes409

10.5.3 Liquid membranes415

10.6 Problems418

11 Quantum Fluids421

11.1 Bose Condensation422

11.2 Superfluidity430

11.2.1 Qualitative features of superfluidity430

11.2.2 Bogoliubov theory of the 4He excitation spectrum439

11.3 Superconductivity442

11.3.1 Cooper problem443

11.3.2 BCS ground state445

11.3.3 Finite-temperature BCS theory449

11.3.4 Landau-Ginzburg theory of superconductivity453

11.4 Problems456

12 Linear Response Theory461

12.1 Exact Results462

12.1.1 Generalized susceptibility and the structure factor462

12.1.2 Thermodynamic properties469

12.1.3 Sum rules and inequalities470

12.2 Mean Field Response472

12.2.1 Dielectric function of the electron gas473

12.2.2 Weakly interacting Bose gas475

12.2.3 Excitations of the Heisenberg ferromagnet477

12.2.4 Screening and plasmons480

12.2.5 Exchange and correlation energy486

12.2.6 Phonons in metals487

12.3 Entropy Production,the Kubo Formula,and the Onsager Rela-tions for Transport Coefficients490

12.3.1 Kubo formula490

12.3.2 Entropy production and generalized currents and forces492

12.3.3 Microscopic reversibility:Onsager relations494

12.4 The Boltzmann Equation498

12.4.1 Fields,drift and collisions498

12.4.2 DC conductivity of a metal500

12.4.3 Thermal conductivity and thermoelectric effects503

12.5 Problems507

13 Disordered Systems513

13.1 Single-Particle States in Disordered Systems515

13.1.1 Electron states in one dimension516

13.1.2 Transfer matrix517

13.1.3 Localization in three dimensions523

13.1.4 Density of states525

13.2 Percolation530

13.2.1 Scaling theory of percolation533

13.2.2 Series expansions and renormalization group536

13.2.3 Rigidity percolation540

13.2.4 Conclusion542

13.3 Phase Transitions in Disordered Materials542

13.3.1 Statistical formalism and the replica trick544

13.3.2 Nature of phase transitions546

13.4 Strongly Disordered Systems551

13.4.1 Molecular glasses552

13.4.2 Spin glasses554

13.4.3 Sherrington-Kirkpatrick model558

13.5 Problems565

A Occupation Number Representation569

Bibliography583

Index603