The random-cluster model
Author(s)
Bibliographic Information
The random-cluster model
(Die Grundlehren der mathematischen Wissenschaften, 333)
Springer, 2009
2nd corr. print.
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The random-cluster model / Geoffrey Grimmett
BA77378096
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The random-cluster model / Geoffrey Grimmett
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Note
Copyright c2006 by Springer
Includes bibliographical references (p. [353]-373) and index
Description and Table of Contents
Description
The random-cluster model has emerged 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. The Random-Cluster Model contains accounts of the subcritical and supercritical phases, together with clear statements of important open problems. The book includes treatment of the first-order (discontinuous) phase transition.
Table of Contents
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.
by "Nielsen BookData"