3 years ago

Random-Cluster Correlation Inequalities for Gibbs Fields

Alberto Gandolfi


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.

Publisher URL: https://link.springer.com/article/10.1007/s10955-018-2130-x

DOI: 10.1007/s10955-018-2130-x

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