The Random-Cluster Model
(Sprache: Englisch)
The random-cluster model has emerged 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. The...
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The random-cluster model has emerged 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. The Random-Cluster Model contains accounts of the subcritical and supercritical phases, together with clear statements of important open problems. The book includes treatment of the first-order (discontinuous) phase transition.
Inhaltsverzeichnis zu „The Random-Cluster Model “
- 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
- Appendix: The Origins of FK(G)
- List of Notation
- References
- Index.
Autoren-Porträt von Geoffrey R. Grimmett
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.
Bibliographische Angaben
- Autor: Geoffrey R. Grimmett
- 2009, 1st Corrected ed. 2006, Corr. 3rd printing 2009., 378 Seiten, Maße: 16 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer
- ISBN-10: 3540328904
- ISBN-13: 9783540328902
- Erscheinungsdatum: 17.07.2009
Sprache:
Englisch
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