COMPARISON AND DISJOINT-OCCURRENCE INEQUALITIES FOR RANDOM-CLUSTER MODELS

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 point p(c)(q) of the random-cluster model with cluster-weighting factor q (greater than or equal to 1) is strictly monotone in q. Our second result is a ''BK inequality'' for the disjoint occurrence of increasing events, in a weaker form than that available in percolation theory.