Random-Cluster Correlation Inequalities for Gibbs Fields

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In this note we prove a correlation inequality for local variables of a Gibbs field based on the connectivity in a random cluster representation of the non overlap configuration distribution of two independent copies of the field. As a consequence, we show that absence of a particular type of percolation (of Machta–Newman–Stein blue bonds) implies uniqueness of Gibbs distribution in EA Spin Glasses. In dimension two this could constitute a step towards a proof that the critical temperature is zero.

Original languageEnglish (US)
Pages (from-to)249-267
Number of pages19
JournalJournal of Statistical Physics
Issue number2
StatePublished - Oct 1 2018


  • Correlation inequalities
  • Disagreement percolation
  • Gibbs fields
  • Random cluster representation
  • Spin glasses

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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