Two-point connectivity of two-dimensional critical $Q-$ Potts random clusters on the torus

Abstract

We consider the two dimensional $Q-$ random-cluster Potts model on the torus and at the critical point. We study the probability for two points to be connected by a cluster for general values of $Q\in [1,4]$. Using a Conformal Field Theory (CFT) approach, we provide the leading topological corrections to the plane limit of this probability. These corrections have universal nature and include, as a special case, the universality class of two-dimensional critical percolation. We compare our predictions to Monte Carlo measurements. Finally, we take Monte Carlo measurements of the torus energy one-point function that we compare to CFT computations.

23 pages, 6 figures. Results added in Section 5.2, Section 5.4 has been clarified and some notation inconsistencies have been fixed