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＜電子ブック＞
The Random-Cluster Model / by Geoffrey R. Grimmett
(Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics. ISSN:21969701 ; 333)

版	1st ed. 2006.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2006
本文言語	英語
大きさ	XIII, 378 p : online resource
著者標目	*Grimmett, Geoffrey R author SpringerLink (Online service)
件　名	LCSH:Probabilities LCSH:Mathematical physics FREE:Probability Theory FREE:Theoretical, Mathematical and Computational Physics
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-540-32891-9

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