Abstract

In this talk we study the random cluster model on essentially large girth and random regular graphs. We give explicit formula for the limiting free entropy of the random cluster model. Our result  extends the work of Dembo, Montanari, Sly and Sun for the Potts model, and we prove a conjecture of Helmuth, Jenssen and Perkins about the phase transition of the random cluster model. This is joint work with Ferenc Bencs and Márton Borbényi.