The Random-Cluster Model [electronic resource] /
Grimmett, Geoffrey R.author.
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.
Description based upon print version of record.
Includes bibliographical references (p. [353]-372) and index.
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.
Probabilities.
Mathematical physics.
Probability Theory and Stochastic Processes.
Theoretical, Mathematical and Computational Physics.
Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete