The random-cluster model

Author(s)

• Grimmett, Geoffrey

Bibliographic Information

The random-cluster model

Geoffrey Grimmett

（Die Grundlehren der mathematischen Wissenschaften, 333）

Springer, c2006

Note

Includes bibliographical references (p. [353]-372) and index

Description and Table of Contents

Description

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.

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.

by "Nielsen BookData"

Details

• NCID: BA77378096
• ISBN:
  • 3540328904
• LCCN: 2006925087
• Country Code: gw
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Berlin
• Pages/Volumes: xiii, 377 p.
• Size: 24 cm
• Classification:
  • SG : 510
  • LCC : QC20.7.S8
• Subject Headings:
  • LCSH : Stochastic processes
  • LCSH : Ferromagnetism
  • LCSH : Phase transformations (Statistical physics)
• Parent Bibliography ID:
  • BA00007422