Gibbs States on Countable Sets

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.

Gibbs states and Markov random fields
Interacting particle systems
Coupled Markov chains
Gibbs states and Markov random fields on countable graphs
Gibbs states on countable sets
Kirkwood-Salsburg equations
Involutions of P(S)
Attractive and supermodular potentials
Attractive pair potentials
Examples of phase transition
The extreme points of Gv
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Gibbs States on Countable Sets

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