Conformal invariance of the planar four-state Potts model and its random-cluster representation

Abstract

For the critical random-cluster model on ${\mathbb{Z}}^2$ with cluster-weight $q=4$, we prove the convergence of loops to CLE(4) in the scaling limit. Conformal invariance of the four-state Potts model is then deduced via the Edwards-Sokal coupling.

arXiv comment14 pages, 5 figures