统计物理学PDF电子书下载

Ⅰ Fundamentals of Statistical Physics 1

1 The Lectures—A Survey 3

1.1 The Journey:Many Different Approaches 3

1.2 The Main Sights 5

1.3 Is the Trip Worthwhile? 9

2 One Particle and Many 11

2.1 Formulation 11

2.2 The Ising Model 12

2.3 N Independent Particles—Quantum Description 13

2.4 Averages From Derivatives 15

2.5 N Independent Particles in a Box 17

2.6 Fluctuations Big and Small 20

2.7 The Problems of Statistical Physics 21

3 Gaussian Distributions 29

3.1 Introduction 29

3.2 One Variable 29

3.3 Many Gaussian Variables 31

3.4 Lattice Green Function 33

3.5 Gaussian Random Functions 35

3.6 Central Limit Theorem 35

3.7 Distribution of Energies 36

3.8 Large Deviations 38

3.9 On Almost Gaussian Integrals 41

3.10 Three Versions of Gaussian Problems 42

4 Quantum Mechanics and Lattices 45

4.1 All of Quantum Mechanics in One Brief Section 45

4.2 From d=1 Models to Quantum Mechanics 46

4.3 An Example:The Linear Ising Chain 48

4.4 One-Dimensional Gaussian Model 51

4.5 Coherence Length 56

4.6 Operator Averages 57

4.7 Correlation Functions 59

4.8 Ising Correlations 60

4.9 Two-Dimensional Ising Model 64

Ⅱ Random Dynamics 69

5 Diffusion and Hopping 71

5.1 Random Walk on a Lattice 71

5.2 Formulating This Problem 73

5.3 The Diffusion of Probability and Particles 76

5.4 From Conservation to Hydrodynamic Equations 79

5.5 Distribution Functions 83

5.6 Cascade Processes and Securities Prices 84

5.7 Reprints on Dynamics 91

5.7.1 Forest and Witten:Smoke Particle Aggregates 92

5.7.2 Witten and Sander:Diffusion Limited Aggregation 101

5.7.3 Kadanoff:Chaos and Complexity 105

6 From Hops to Statistical Mechanics 119

6.1 Random Walk in Momentum 120

6.2 The Diffusion Equation Again 123

6.3 Time Dependence of Probability 124

6.4 Time Dependence in Deterministic Case 126

6.5 Equilibrium Solutions 128

6.6 Back to Collisions 131

6.7 From Fokker-Planck to Equilibrium 133

6.8 Properties of Fokker-Planck Equation 135

6.9 Reprints on Organization 138

6.9.1 Chao Tang et al.:Phase Organization 139

6.9.2 Baket al.:Self-Organized Criticality 143

6.9.3 Carlson et al.:Singular Diffusion 147

6.9.4 Jaeger et al.:Experimental Studies 151

7 Correlations and Response 155

7.1 Time Independent Response 155

7.2 Hamiltonian Time-Dependence 158

7.3 Sum Rules 161

7.4 Non-Interacting Particles 163

7.5 Plasma Behavior 164

Ⅲ More Statistical Mechanics 169

8 Statistical Thermodynamics 171

8.1 The Chemical Potential Defined 171

8.2 Barometer Formula 173

8.3 Sharing Energy 174

8.4 Ensemble Theory 179

8.5 Temperatures and Energy Flow 182

9 Fermi,Bose,and Other 187

9.1 Quantum Formulation 187

9.2 Statistical Mechanics of Non-Interacting Degenerate Particles 188

9.3 The Non-Degenerate Limit 191

9.4 Degenerate Fermions 192

9.5 Degenerate Bosons Ⅰ.Photons and Phonons 196

9.6 Degenerate Bosons Ⅱ.One-Dimensional Phonons 198

9.7 Degenerate Bosons Ⅲ.Bose Phase Transition 201

9.8 Entropies 203

Ⅳ Phase Transitions 207

10 Overview of Phase Transitions 209

10.1 Thermodynamic Phases 209

10.2 Phase Transitions 210

10.3 Two Kinds of Transitions 211

10.4 Back to the Ising Model 214

10.5 Mean Field Theory of Magnets 215

10.6 The Phases 216

10.7 Low Temperature Result 218

10.8 Free Energy Selection Argument 219

10.9 Behaviors of Different Phases 221

11 Mean Field Theory of Critical Behavior 225

11.1 The Infinite Range Model 226

11.2 Mean Field Theory Near the Critical Point 227

11.3 Critical Indices 230

11.4 Scaling Function for Magnetization 231

11.5 Spatial Correlations 232

11.6 Analyticity 238

11.7 Mean Field Theory for the Free Energy 239

11.8 When Mean Field Theory Fails 242

12 Continuous Phase Transitions 247

12.1 Historical Background 247

12.2 Widom Scaling Theory 248

12.3 The Ising Model:Rescaled 252

12.4 Fixed Points 257

12.5 Phenomenology of Scaling Fields 258

12.6 Theory of Scaling Fields 259

12.7 Scaling Relations for Operators 262

12.8 Transforming Operators 266

12.9 Universality 266

12.10 Operator Product Expansions 267

12.11 Reprints on Critical Correlations 268

12.11.1 Kadanoff:Correlations Along a Line 269

12.11.2 Kadanoff-Wegner:Marginal Behavior 274

13 Renormalization in One Dimension 279

13.1 Introduction 279

13.2 Decimation 279

13.3 The Ising Example 280

13.4 Phase Diagrams,Flow Diagrams,and the Coherence Length 281

13.5 The Gaussian Model 283

13.6 Analysis of Recursion Relation 284

13.7 Fixed Point Analysis for the Gaussian Model 285

13.8 Two-Dimensional Ising Model 288

14 Real Space Renormalization Techniques 291

14.1 Introduction 291

14.2 Decimation:An Exact Calculation 292

14.3 The Method of Neglect 294

14.4 Potential Moving 295

14.5 Further Work 298

14.6 Reprints on Real Space RG 298

14.6.1 Niemeijer and van Leeuwen:Triangular Lattice R.G 299

14.6.2 David Nelson's Early Summary 303

14.6.3 Kadanoff:Bond-moving,and a Variational Method 308

14.6.4 Kadanoff:Migdal's Simple and Versatile Method 312

14.6.5 Migdal's Original Papers 348

15 Duality 359

15.1 Doing Sums 359

15.2 Two Dimensions 361

15.3 Direct Coupling and Dual Coupling 363

15.4 Two-Dimensional Calculation 365

15.5 Ising Model 368

15.6 XY is Connected to SOS 369

15.7 Gaussian goes into Gaussian 371

15.8 Dual Correlations 371

16 Planar Model and Coulomb Systems 377

16.1 Why Study a Planar Model? 377

16.2 One-Dimensional Case 379

16.3 Phases of the Planar Model 380

16.4 The Gaussian Approximation 382

16.5 Two-Dimensional Coulomb Systems 386

16.6 Multipole Expansion 387

16.7 Reprint on Spin Waves 390

16.7.1 V.L.Berezinskii:An Overview of Problems with Continuous Symmetry 391

17 XY Model,Renormalization,and Duality 399

17.1 Plan of Action 399

17.2 Villain Representation of the Basic Bonds 400

17.3 Duality Transformation 401

17.4 Two Limits 402

17.5 Vortex Representation 403

17.6 The Magnetically Charged System 405

17.7 Correlation Calculation 408

17.8 The Renormalization Calculation 409

17.9 Spatial Averages 411

17.10 The Actual Renormalization 413

17.11 Reprints on Planar Model 415

17.11.1 The Kosterlitz-Thouless Theory 416

17.11.2 Kosterlitz:On Renormalization of the Planar Model 439

17.11.3 Jorge V.José,Leo P.Kadanoff,Scott Kirkpatrick,David R.Nelson:Renormalization and Vortices 454

Index 479