Gibbs States on Countable Sets

Erscheinungsjahr 2008
ISBN: 978-0-521-09011-7
Verlag: Cambridge University Press

Buch, Englisch, Band 68, 138 Seiten, Format (B × H): 140 mm x 216 mm, Gewicht: 186 g

Reihe: Cambridge Tracts in Mathematics

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.

Autoren/Hrsg.

Preston, Christopher J.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

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.