A new proof of first order phase transition for the planar random-cluster and Potts models with $qgg1$ (Stochastic Analysis on Large Scale Interacting Systems)

Abstract

We provide a proof that the random-cluster model on the square lattice undergoes a discontinuous phase transition for large values of the cluster-weight q. This implies discontinuity of the phase transition for Potts model on the square lattice provided that the number of colors q is large enough. Let us remind the reader that this result is classical and that we simply provide an alternative approach based on the loop representation.