The percolation signature of the spin glass transition

J. MacHta, C. M. Newman, D. L. Stein

Research output: Contribution to journalArticlepeer-review


Magnetic ordering at low temperature for Ising ferromagnets manifests itself within the associated Fortuin-Kasteleyn (FK) random cluster representation as the occurrence of a single positive density percolating network. In this paper we investigate the percolation signature for Ising spin glass ordering-both in short-range (EA) and infinite-range (SK) models-within a two-replica FK representation and also within the different Chayes-Machta-Redner two-replica graphical representation. Based on numerical studies of the ±J EA model in three dimensions and on rigorous results for the SK model, we conclude that the spin glass transition corresponds to the appearance of two percolating clusters of unequal densities.

Original languageEnglish (US)
Pages (from-to)113-128
Number of pages16
JournalJournal of Statistical Physics
Issue number1
StatePublished - Jan 2008


  • Cluster algorithms
  • Fortuin-Kasteleyn
  • Graphical representations
  • Ising spin glass
  • Percolation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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