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The Random-Cluster Model [electronic resource] /by Geoffrey R. Grimmett.

by Grimmett, Geoffrey R [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Grundlehren der mathematischen Wissensch: 333Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.Description: XIII, 377 p. 37 illus. online resource.ISBN: 9783540328919.Subject(s): Mathematics | Distribution (Probability theory) | Mathematics | Probability Theory and Stochastic Processes | Theoretical, Mathematical and Computational PhysicsDDC classification: 519.2 Online resources: Click here to access online
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.
In: Springer eBooksSummary: 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.
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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.

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