Random-cluster correlation inequalities for Gibbs fields
arXiv:1804.04247 · doi:10.1007/s10955-018-2130-x
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.
arXiv comment23 pages