Random-Cluster Model

The randomcluster model has emerged in recent years as a key tool in themathematical study of ferromagnetism. It may be viewed as an extension ofpercolation to ... » 

The randomcluster model has emerged in recent years as a key tool in themathematical study of ferromagnetism. It may be viewed as an extension ofpercolation to include Ising and Potts models and its analysis is a mix ofarguments from probability and geometry. This systematic study includesaccounts of the subcritical and supercritical phases together with clearstatements of important open problems. There is an extensive treatment of thefirstorder discontinuous phase transition as well as a chapter devoted toapplications of the randomcluster method to other models of statisticalphysics. TOCRandomCluster Measures. Monotonic Measures. FundamentalProperties. InfiniteVolume Measures. Phase Transition. In Two Dimensions.Duality in Higher Dimensions. Dynamics of RandomCluster Models. Flows inPoisson Graphs. On Other Graphs. Graphical Methods for Spin Systems.Appendix The Origins of FKG. List of Notation. References. Index. «