Three- and four-point connectivities of two-dimensional critical $Q-$ Potts random clusters on the torus

Abstract

In a recent paper, we considered the effects of the torus lattice topology on the two-point connectivity of $Q-$ Potts clusters. These effects are universal and probe non-trivial structure constants of the theory. We complete here this work by considering the torus corrections to the three- and four-point connectivities. These corrections, which depend on the scale invariant ratios of the triangle and quadrilateral formed by the three and four given points, test other non-trivial structure constants. We also present results of Monte Carlo simulations in good agreement with our predictions.

30 pages, 9 figures. Figure captions have been added, the notation in section 3.2 has been slightly changed, and typos in equations (4.21) and (5.3) have been corrected