The Random-Cluster Model

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Grundlehren der mathematischen Wissenschaften 333

ISBN: 3642069436
ISBN 13: 9783642069437
Autor: Grimmett, Geoffrey R
Verlag: Springer Verlag GmbH
Umfang: xiii, 378 S., 37 s/w Illustr.
Erscheinungsdatum: 17.11.2010
Auflage: 1/2006
Produktform: Kartoniert
Einband: KT

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.

Artikelnummer: 1537819 Kategorie:

Beschreibung

InhaltsangabeRandom-Cluster Measures.- Monotonic Measures.- Fundamental Properties.- Infinite-Volume Measures.- Phase Transition.- In Two Dimensions.- Duality in Higher Dimensions.- Dynamics of Random-Cluster Models.- Flows in Poisson Graphs.- On Other Graphs.- Graphical Methods for Spin Systems.

Inhaltsverzeichnis

Random-Cluster Measures.- Monotonic Measures.- Fundamental Properties.- Infinite-Volume Measures.- Phase Transition.- In Two Dimensions.- Duality in Higher Dimensions.- Dynamics of Random-Cluster Models.- Flows in Poisson Graphs.- On Other Graphs.- Graphical Methods for Spin Systems.- Appendix: The Origins of FK(G).- List of Notation.- References.- Index.

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