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.
KeywordsCorrelation inequalities Gibbs fields Random cluster representation Disagreement percolation Spin glasses
Mathematics Subject Classification60G60 60J99 82B44 82D30
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