Statistical Mechanics - Physics at Oregon State University

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IV CONTENTS 4.3 Gas of poly-atomic molecules. . . . . . . . . . . . . . . . . . . . . 77 4.4 Degenerate gas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.5 Fermi gas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.6 Boson gas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 4.7 Problems for chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . 87 5 Fermions and Bosons 89 5.1 Fermions in a box. . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.2 Bosons in a box. . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 5.3 Bose-Einstein condensation. . . . . . . . . . . . . . . . . . . . . . 113 5.4 Problems for chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . 115 6 Density matrix formalism. 119 6.1 Density operators. . . . . . . . . . . . . . . . . . . . . . . . . . . 119 6.2 General ensembles. . . . . . . . . . . . . . . . . . . . . . . . . . . 123 6.3 Maximum entropy principle. . . . . . . . . . . . . . . . . . . . . . 125 6.4 Equivalence of entropy definitions for canonical ensemble. . . . . 134 6.5 Problems for chapter 6 . . . . . . . . . . . . . . . . . . . . . . . . 136 7 Classical statistical mechanics. 139 7.1 Relation between quantum and classical mechanics. . . . . . . . . 139 7.2 Classical formulation of statistical mechanical properties. . . . . 142 7.3 Ergodic theorem. . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 7.4 What is chaos? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 7.5 Ideal gas in classical statistical mechanics. . . . . . . . . . . . . . 149 7.6 Normal systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 7.7 Quadratic variables. . . . . . . . . . . . . . . . . . . . . . . . . . 151 7.8 Effects of the potential energy. . . . . . . . . . . . . . . . . . . . 152 7.9 Problems for chapter 7 . . . . . . . . . . . . . . . . . . . . . . . . 154 8 Mean Field Theory: critical temperature. 157 8.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 8.2 Basic Mean Field theory. . . . . . . . . . . . . . . . . . . . . . . . 161 8.3 Mean Field results. . . . . . . . . . . . . . . . . . . . . . . . . . . 164 8.4 Density-matrix approach (Bragg-Williams approximation. . . . . 168 8.5 Critical temperature in different dimensions. . . . . . . . . . . . . 177 8.6 Bethe approximation. . . . . . . . . . . . . . . . . . . . . . . . . 181 8.7 Problems for chapter 8 . . . . . . . . . . . . . . . . . . . . . . . . 188 9 General methods: critical exponents. 191 9.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 9.2 Integration over the coupling constant. . . . . . . . . . . . . . . . 192 9.3 Critical exponents. . . . . . . . . . . . . . . . . . . . . . . . . . . 197 9.4 Relation between susceptibility and fluctuations. . . . . . . . . . 203 9.5 Exact solution for the Ising chain. . . . . . . . . . . . . . . . . . 205 9.6 Spin-correlation function for the Ising chain. . . . . . . . . . . . . 210
CONTENTS V 9.7 Renormalization group theory. . . . . . . . . . . . . . . . . . . . 218 9.8 Problems for chapter 9 . . . . . . . . . . . . . . . . . . . . . . . . 226 A Solutions to selected problems. 229 A.1 Solutions for chapter 1. . . . . . . . . . . . . . . . . . . . . . . 229 A.2 Solutions for chapter 2. . . . . . . . . . . . . . . . . . . . . . . 237 A.3 Solutions for chapter 3 . . . . . . . . . . . . . . . . . . . . . . . 242 A.4 Solutions for chapter 4. . . . . . . . . . . . . . . . . . . . . . . 247 A.5 Solutions for chapter 5. . . . . . . . . . . . . . . . . . . . . . . 251 A.6 Solutions for chapter 6. . . . . . . . . . . . . . . . . . . . . . . 257
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140 CHAPTER 7. CLASSICAL STATISTICA
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230 APPENDIX A. SOLUTIONS TO SELECT
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Statistical Mechanics - Physics at Oregon State University

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