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Two-point connectivity of two-dimensional critical $Q-$ Potts random clusters on the torus
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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.
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Logarithmic operators in $c=0$ bulk CFTs
The bulk energy four-point function in percolation and self-avoiding walk CFTs is non-zero at c=0, driven by coupling to a rank-3 Jordan block associated with the second energy operator.
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