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

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 is an element of [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.