The Random-Cluster Model

• Κύριος συγγραφέας: Grimmett, Geoffrey R. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.
• Σειρά: Grundlehren der mathematischen Wissensch, 333
• Θέματα: Mathematics.; Probabilities.; Physics.; Probability Theory and Stochastic Processes.; Theoretical, Mathematical and Computational Physics.
• Φυσική περιγραφή: XIII, 378 p. online resource.
• ISBN: 9783540328919
• ISSN: 0072-7830 ;

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.