The Random-Cluster Model
Part of the Grundlehren der mathematischen Wissensch book series (GL, volume 333)
About this book
Introduction
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.
Keywords
Ising model Potts model Random-cluster model ferromagnetism geometry percolation
Bibliographic information
- DOI https://doi.org/10.1007/978-3-540-32891-9
- Copyright Information Springer Berlin Heidelberg 2006
- Publisher Name Springer, Berlin, Heidelberg
- eBook Packages Mathematics and Statistics
- Print ISBN 978-3-540-32890-2
- Online ISBN 978-3-540-32891-9
- Series Print ISSN 0072-7830
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