E-Book 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.
E-Book Content
METHODS OF STATISTICAL PHYSICS This graduate-level textbook 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, specific heat, Helmholtz potential, magnetic susceptibility, and phase transitions of macroscopic systems. In addition to the more standard material covered, this book also describes more powerful techniques, which are not found elsewhere, to determine the correlation effects on which the 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 this method to topics such as the three-dimensional Ising model, BCS superconductivity, the Heisenberg ferromagnet, the ground state energy of the Anderson model, antiferromagnetism within the Hubbard model, and propagation of short range order, are extensively discussed. Important identities relating different correlation functions of the Ising model are also derived. Although a basic knowledge of quantum mechanics is required, the mathematical formulation is accessible, and the correlation functions can