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The random-cluster model

Author: Geoffrey Grimmett
Publisher: Berlin ; New York : Springer, ©2006.
Series: Grundlehren der mathematischen Wissenschaften, 333.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
"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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Grimmett, Geoffrey.
Random-cluster model.
Berlin ; New York : Springer, ©2006
(DLC) 2006925087
(OCoLC)70177985
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Geoffrey Grimmett
ISBN: 9783540328919 3540328912 3540328904 9783540328902 661071682X 9786610716821
OCLC Number: 262691034
Description: 1 online resource (xiii, 377 pages) : illustrations.
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 --
Appendix: The Origins of FK(G) --
List of Notation --
References --
Index.
Series Title: Grundlehren der mathematischen Wissenschaften, 333.
Responsibility: Geoffrey Grimmett.
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Abstract:

The random-cluster model has emerged as a key tool in the mathematical study of ferromagnetism. The Random-Cluster Model contains accounts of the subcritical and supercritical phases, together with  Read more...

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From the reviews:"This book constitutes an authoritative treatise of the random cluster model and its applications. It will be indispensable for anyone working on this and related subjects and can Read more...

 
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