On four-point connectivities in the critical 2d Potts model

Marco Picco, Sylvain Ribault, Raoul Santachiara

SciPost Phys. 7, 044 (2019) · published 7 October 2019


We perform Monte-Carlo computations of four-point cluster connectivities in the critical 2d Potts model, for numbers of states $Q\in (0,4)$ that are not necessarily integer. We compare these connectivities to four-point functions in a CFT that interpolates between D-series minimal models. We find that 3 combinations of the 4 independent connectivities agree with CFT four-point functions, down to the $2$ to $4$ significant digits of our Monte-Carlo computations. However, we argue that the agreement is exact only in the special cases $Q=0, 3, 4$. We conjecture that the Potts model can be analytically continued to a double cover of the half-plane $\{\Re c <13\}$, where $c$ is the central charge of the Virasoro symmetry algebra.

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Conformal field theory (CFT) Monte-Carlo simulations Potts model Virasoro algebras

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