Correlation inequalities of GKS type for the Potts model

Abstract

Correlation inequalities are presented for ferromagnetic Potts models with external field, using the random cluster representation of Fortuin and Kasteleyn, together with the FKG inequality. These results extend and simplify earlier inequalities of Ganikhodjaev and Razak, and also of Schonmann, and include GKS-type inequalities when the spin-space is taken as the set of qth roots of unity.