Abstract
A principal technique for studying percolation, (ferromagnetic) Ising, Potts, and random-cluster models is the FKG inequality, which implies certain stochastic comparison inequalities for the associated probability measures. The first result of this paper is a new comparison inequality, proved using an argument developed elsewhere in order to obtain strict inequalities for critical values. As an application of this inequality, we prove that the critical pointp c (q) of the random-cluster model with cluster-weighting factorq (≥1) is strictly monotone inq. Our second result is a “BK inequality” for the disjoint occurrence of increasing events, in a weaker form than that available in percolation theory.
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Grimmett, G. Comparison and disjoint-occurrence inequalities for random-cluster models. J Stat Phys 78, 1311–1324 (1995). https://doi.org/10.1007/BF02180133
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DOI: https://doi.org/10.1007/BF02180133