Two-point connectivity of two-dimensional critical \(Q\)-Potts random clusters on the torus. (English) Zbl 1459.82047
Summary: 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.
MSC:
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
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