This book may be used as a textbook for the first or second year graduate student who is studying concurrently such topics as theory of complex analysis, classical mechanics, classical electrodynamics, and quantum mechanics. In a textbook on statistical mechanics, it is common practice to deal with two im-portant areas of the subject: mathematical formulation of the distribution laws of sta- tistical mechanics, and demonstrations of the applicability of statistical mechanics.

Preface

Acknowledgements

1 The laws of thermodynamics

 1.1 The thermodynamic system and processes

 1.2 The zeroth law of thermodynamics

 1.3 The thermal equation of state

 1.4 The classical ideal gas

 1.5 The quasistatic and reversible processes

 1.6 The first law of thermodynamics

 1.7 The heat capacity

 1.8 The isothermal and adiabatic processes

 1.9 The enthalpy

 1.10 The second law of thermodynamics

 1.11 The Carnot cycle

 1.12 The thermodynamic temperature

 1.13 The Camot cycle of an ideal gas

 1.14 The Clausius inequality

 1.15 The entropy

 1.16 General integrating factors

 1.17 The integrating factor and cyclic processes

 1.18 Hausen's cycle

 1.19 Employnent of the second law of thermodynamics

 1.20 The universal i tegrating factor Exercises

2 Thermodynamic relations

 2.1 Thermodynamic potentials

 2.2 Maxwell relations

……

3 The ensemble theory

4 System Hamitonians

5 The density matrix

6 The cluster variation method

7 Infintite-series reprentaions of correlation functions

8 The extended mean-field approximation

9 The exact Ising lattice identities

10 Propagatinon of short range order

11 Phase transition of the two-dimensional Ising model

Appendix1 The gamma function

Appendix2 The critical exponent in the tetrahedron approximation

Appendix3 Programming organizationo of cluster variation method

Appendix4 Aunitary transformation applied to the Hubbard Hamiltomina

Appendix5 Exact Ising identities on the diamond lattice

Refernces

Bibliography

Index