The Random-Cluster Model

  • Geoffrey R. Grimmett

Part of the Grundlehren der mathematischen Wissensch book series (GL, volume 333)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Pages 19-36
  3. Pages 98-132
  4. Pages 133-166
  5. Pages 257-275
  6. Pages 276-319
  7. Back Matter
    Pages 341-379

About this book


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.


Ising model Potts model Random-cluster model ferromagnetism geometry percolation

Authors and affiliations

  • Geoffrey R. Grimmett
    • 1
  1. 1.Statistical Laboratory, Centre for Mathematical SciencesUniversity of CambridgeCambridgeUK

Bibliographic information