Gibbs States on Countable Sets

by Christopher J. Preston

Overview

The book is an introduction to some of the 1967–1974 results and techniques in classical lattice statistical mechanics. It is written in the language of probability theory rather than that of physics, and is thus aimed primarily at mathematicians who might have little or no background in physics. This area of statistical mechanics is presently enjoying a rapid growth and the book should allow a graduate student or research mathematician to find out what is happening in it. The book is self-contained except for some basic concepts of probability theory, and can be read by any undergraduate student in mathematics who has a reasonable background in probability.

Product Details

ISBN-13:	9780521090117
Publisher:	Cambridge University Press
Publication date:	11/13/2008
Series:	Cambridge Tracts in Mathematics , #68
Pages:	140
Product dimensions:	5.50(w) x 8.40(h) x 0.60(d)

Table of Contents

1. Gibbs states and Markov random fields; 2. Interacting particle systems; 3. Coupled Markov chains; 4. Gibbs states and Markov random fields on countable graphs; 5. Gibbs states on countable sets; 6. Kirkwood–Salsburg equations; 7. Involutions of P(S); 8. Attractive and supermodular potentials; 9. Attractive pair potentials; 10. Examples of phase transition; 11. The extreme points of Gv.