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

Abstract

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.

53 pages, v2: small improvements and clarifications