Comparison and disjoint-occurrence inequalities for random-cluster models
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 point p c ( q) of the random-cluster model with cluster-weighting factor q (≥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.
- Publication:
-
Journal of Statistical Physics
- Pub Date:
- March 1995
- DOI:
- 10.1007/BF02180133
- Bibcode:
- 1995JSP....78.1311G
- Keywords:
-
- Random-cluster model;
- Ising model;
- Potts model;
- comparison inequality;
- BK inequality;
- FKG inequality