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arXiv · 1804.04247

Random-cluster correlation inequalities for Gibbs fields

Alberto Gandolfi
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Abstract

In this note we prove a correlation inequality for local variables of a Gibbs field based on the connectivity by active hyperbonds 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 Machta-Newman-Stein blue bonds percolation 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.

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Alberto Gandolfi. 2018-04-11. Random-cluster correlation inequalities for Gibbs fields. https://doi.org/10.1007/s10955-018-2130-x

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