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

• Published in: SciPost physics Vol. 7; no. 4; p. 044
• Main Authors: Picco, Marco, Ribault, Sylvain, Santachiara, Raoul
• Format: Journal Article
• Language: English
• Published: SciPost Foundation 01.10.2019; SciPost
• Subjects: General Physics; High Energy Physics - Theory; Mathematical Physics; Physics; field theory: conformal; model: minimal; cluster; n-point function: 4; Monte Carlo; central charge: Virasoro; symmetry: Virasoro; symmetry: algebra; Potts model
• ISSN: 2542-4653; 2542-4653
• DOI: 10.21468/SciPostPhys.7.4.044

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 2 2 to 4 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 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\} { ℜ c < 13 } , where c c is the central charge of the Virasoro symmetry algebra.