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The random-cluster model

Author: Geoffrey Grimmett
Publisher: Dordrecht ; New York : Springer, ©2006
Series: Grundlehren der mathematischen Wissenschaften, 333.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
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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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Geoffrey Grimmett
ISBN: 3540328904 9783540328902 3642069436 9783642069437
OCLC Number: 70177985
Description: xiii, 378 pages : illustrations ; 24 cm.
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.
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. It may be viewed as an extension of percolation to include Ising and Potts models, and its analysis is  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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