Gibbs States on Countable Sets

Christopher J. Preston

doi:10.1017/CBO9780511897122

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.

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Contents

Frontmatter
pp i-iv
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Contents
pp v-vi
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Preface
pp vii-x
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1 - Gibbs states and Markov random fields
pp 1-9
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2 - Interacting particle systems
pp 10-18
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3 - Coupled Markov chains
pp 19-24
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4 - Gibbs states and Markov random fields on countable graphs
pp 25-32
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5 - Gibbs states on countable sets
pp 33-45
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6 - Kirkwood–Salsburg equations
pp 46-51
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7 - Involutions of P(S)
pp 52-59
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8 - Attractive and supermodular potentials
pp 60-72
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9 - Attractive pair potentials
pp 73-90
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10 - Examples of phase transition
pp 91-105
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11 - 11 The extreme points of GV
pp 106-114
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Appendix The Lee-Yang circle theorem revisited
pp 115-122
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Bibliography
pp 123-126
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Index
pp 127-128
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Gibbs States on Countable Sets

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-x

1 - Gibbs states and Markov random fields
pp 1-9

2 - Interacting particle systems
pp 10-18

3 - Coupled Markov chains
pp 19-24

4 - Gibbs states and Markov random fields on countable graphs
pp 25-32

5 - Gibbs states on countable sets
pp 33-45

6 - Kirkwood–Salsburg equations
pp 46-51

7 - Involutions of P(S)
pp 52-59

8 - Attractive and supermodular potentials
pp 60-72

9 - Attractive pair potentials
pp 73-90

10 - Examples of phase transition
pp 91-105

11 - 11 The extreme points of GV
pp 106-114

Appendix The Lee-Yang circle theorem revisited
pp 115-122

Bibliography
pp 123-126

Index
pp 127-128

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Gibbs States on Countable Sets

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