Methods of Statistical Physics

by Tomoyasu Tanaka

Overview

This text by one of the originators of the cluster variation method of statistical mechanics is aimed at second- and third-year graduate students studying such topics as the theory of complex analysis, classical mechanics, classical electrodynamics, and quantum mechanics. The central theme is that, given the Hamiltonian for a system, it is possible to calculate the thermodynamics correlation function, either numerically or through the use of infinite series. The book is self-contained, with all required mathematics included either in the text or in Appendixes. The text includes many exercises designed for self-study.

Product Details

ISBN-13:	9780521580564
Publisher:	Cambridge University Press
Publication date:	03/14/2002
Pages:	310
Product dimensions:	7.13(w) x 10.04(h) x 0.83(d)

Table of Contents

1. Laws of thermodynamics; 2. Thermodynamic relations; 3. The ensemble theory; 4. System Hamiltonians; 5. The density matrix; 6. The cluster variation method; 7. Infinite series representations of correlation functions; 8. The extended mean-field approximation; 9. The exact Ising lattice identities; 10. Propagation of short range order; 11. Phase transition of the two-dimensional Ising model; Appendix 1. The gamma function; Appendix 2. The critical exponent in the tetrahedron approximation; Appendix 3. Programming organization of the cluster variation method; Appendix 4. A unitary transformation applied to the Hubbard Hamiltonian; Appendix 5. Exact Ising identities on the diamond lattice; References; Subject index.

Editorial Reviews

This graduate-level text on thermal physics covers classical thermodynamics, statistical mechanics, and their applications. It describes theoretical methods to calculate thermodynamic properties, such as the equation of state and specific heat, and describes techniques to determine the correlation effects on which thermodynamic properties are based. Particular emphasis is given to the cluster variation method and a novel formulation is developed for its expression in terms of correlation functions. Applications of the method to areas such as BCS superconductivity and the Heisenberg ferromagnet are derived. A basic knowledge of quantum mechanics is required. Tanaka is professor emeritus of physics and astronomy at Ohio University and also at Chubu University, Japan. Annotation c. Book News, Inc., Portland, OR (booknews.com)

'Each chapter in the book ends with challenging exercises for the student. The mathematics are set out clearly with a type that is clear, in a font that is easily read.' Contemporary Physics

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