Statistical Mechanics of Lattice Systems: Volume 2: Exact, Series and Renormalization Group Methods / Edition 1

by David Lavis, George M. Bell

Overview

Most of the interesting and difficult problems in statistical mechanics arise when the constituent particles of the system interact with each other with pair or multipartiele energies. The types of behaviour which occur in systems because of these interactions are referred to as cooperative phenomena giving rise in many cases to phase transitions. This book and its companion volume (Lavis and Bell 1999, referred to in the text simply as Volume 1) are princi­ pally concerned with phase transitions in lattice systems. Due mainly to the insights gained from scaling theory and renormalization group methods, this subject has developed very rapidly over the last thirty years. ' In our choice of topics we have tried to present a good range of fundamental theory and of applications, some of which reflect our own interests. A broad division of material can be made between exact results and approximation methods. We have found it appropriate to inelude some of our discussion of exact results in this volume and some in Volume 1. Apart from this much of the discussion in Volume 1 is concerned with mean-field theory. Although this is known not to give reliable results elose to a critical region, it often provides a good qualitative picture for phase diagrams as a whole. For complicated systems some kind of mean-field method is often the only tractable method available. In this volume our main concern is with scaling theory, algebraic methods and the renormalization group.

Product Details

ISBN-13:	9783642084102
Publisher:	Springer Berlin Heidelberg
Publication date:	12/07/2010
Series:	Theoretical and Mathematical Physics
Edition description:	Softcover reprint of hardcover 1st ed. 1999
Pages:	430
Product dimensions:	6.10(w) x 9.25(h) x 0.24(d)

Table of Contents

1. Thermodynamics and Statistical Mechanics.- 2. Phase Transitions and Scaling Theory.- 3. Landau and Landau-Ginzburg Theory.- 4. Algebraic Methods in Statistical Mechanics.- 5. The Eight-Vertex Model.- 6. Real-Space Renormalization Group Theory.- 7. Series Methods.- 8. Dimer Assemblies.- A. Appendices.- References and Author Index.