ENGLISH

The Random-Cluster Model

By Geoffrey R. Grimmett

Book information

Publisher
Springer
Year
2009
ISBN
9783540328902, 3-540-32890-4
ISSN
0072-7830
Language
english
Format
PDF
Filesize
5 MB (4790995 bytes)
Series
Grundlehren der mathematischen Wissenschaften 333
Edition
1st ed. 2006. Corr. 2nd printing
Pages
390\390
Topic
Physics
Library
mexmat
Time added
2009-07-20 03:45:11

Description

The random-cluster model has emerged in recent years as a key tool in the mathematical study of ferromagnetism. It may be viewed as an extension of percolation to include Ising and Potts models, and its analysis is a mix of arguments from probability and geometry. This systematic study includes accounts of the subcritical and supercritical phases, together with clear statements of important open problems. There is an extensive treatment of the first-order (discontinuous) phase transition, as well as a chapter devoted to applications of the random-cluster method to other models of statistical physics.

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