Archive ouverte HAL – On four-point connectivities in the critical 2d Potts model

Marco Picco 1 Sylvain Ribault 2 Raoul Santachiara 3

Marco Picco, Sylvain Ribault, Raoul Santachiara. On four-point connectivities in the critical 2d Potts model. SciPost Phys., 2019, 7, pp.044. ⟨10.21468/SciPostPhys.7.4.044⟩. ⟨hal-02166498⟩

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.

• 1. LPTHE - Laboratoire de Physique Théorique et Hautes Energies
• 2. IPHT - Institut de Physique Théorique - UMR CNRS 3681
• 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques