A remark on gauge symmetries in Ising spin glasses

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This paper studies a particular line in the parameter space of the FK random interaction random cluster model for spin glasses following Katsura ([K]) and Mazza ([M]). We show that, after averaging over the random couplings, the occupied FK bonds have exactly a Bernoulli distribution. Comparison with explicit calculations on trees confirms the marginal role of FK percolation in determining phase transitions.

Original languageEnglish (US)
Pages (from-to)419-430
Number of pages12
JournalProbability Theory and Related Fields
Issue number4
StatePublished - Aug 1999


  • FK model
  • Gauge invariance
  • Percolation
  • Spin glasses

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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