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This title in other editionsOther titles in the Cambridge Tracts in Mathematics series:
Cambridge Tracts in Mathematics #68: Gibbs States on Countable Setsby Christopher J. Preston
Synopses & ReviewsPublisher Comments:The book is an introduction to some of the 19671974 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 selfcontained 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.
Table of Contents1. 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. KirkwoodSalsburg 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.
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