Geoffrey R. Grimmett

The Random-Cluster Model

Ebook (PDF Format)

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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Produktdetails

ISBN: 978-3-540-32891-9
EAN: 9783540328919
Produktnummer: 12826047
Verlag: Springer-Verlag GmbH
Sprache: Englisch
Erscheinungsjahr: 2006
Plattform: PDF
Masse: 5'661 KB
Auflage: 2006

Über den Autor

PhD (Oxford 1974) under supervision of John Hammersley and Dominic Welsh. Member of the Mathematics Department of Bristol University (1976-1992), and subsequently appointed to the Professorship of Mathematics Statistics at Cambridge University. Author of around 100 articles and five books in probability and related fields, including Percolation (Springer 1999), Probability and Random Processes (with David Stirzaker, Oxford University Press 2001). Managing Editor of Probability Theory and Related Fields, 2001-2005.