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

## TL;DR

This paper investigates the probability of two points being connected in the 2D critical Q-Potts model on a torus, using conformal field theory and Monte Carlo simulations to analyze universal topological corrections.

## Contribution

It provides the first analytical derivation of topological corrections to connection probabilities in the Q-Potts model at criticality, validated by Monte Carlo data.

## Key findings

- Universal topological corrections are derived for connection probabilities.
- Monte Carlo results agree with conformal field theory predictions.
- The study extends understanding of critical phenomena 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.