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

TL;DR

This paper investigates how the topology of a torus affects three- and four-point connectivities in two-dimensional critical Q-Potts clusters, revealing universal corrections that test non-trivial structure constants, supported by Monte Carlo simulations.

Contribution

It extends previous work by analyzing three- and four-point connectivities on the torus, providing universal correction formulas and validating them with simulations.

Findings

Universal torus corrections depend on scale-invariant ratios.

Monte Carlo simulations agree with theoretical predictions.

Results probe non-trivial structure constants of the theory.

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.