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 probabi lity measures. The first result of this paper is a new comparison ineq uality, proved using an argument developed elsewhere in order to obtai n strict inequalities for critical values. As an application of this i nequality, we prove that the critical point p(c)(q) of the random-clus ter model with cluster-weighting factor q (greater than or equal to 1) is strictly monotone in q. Our second result is a ''BK inequality'' f or the disjoint occurrence of increasing events, in a weaker form than that available in percolation theory.