The Random-Cluster Model

• Main Author: Grimmett, Geoffrey R. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.
• Series: Grundlehren der mathematischen Wissensch, 333
• Subjects: Mathematics.; Probabilities.; Physics.; Probability Theory and Stochastic Processes.; Theoretical, Mathematical and Computational Physics.

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 acco...

Table of 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.