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)Q∈(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 22 to 44 significant digits of our Monte-Carlo computations. However, we argue that the agreement is exact only in the special cases Q=0, 3, 4Q=0,3,4. We conjecture that the Potts model can be analytically continued to a double cover of the half-plane \{\Re c <13\}{ℜc<13}, where cc is the central charge of the Virasoro symmetry algebra.