Potts correlators and the static three-quark potential

TL;DR

This paper analyzes two- and three-point correlators in the 2D three-state Potts model using form factors and conformal field theory, comparing predictions with Monte Carlo simulations to understand the three-quark potential behavior.

Contribution

It provides a detailed comparison between theoretical predictions and high-precision Monte Carlo data for correlators, determining non-universal constants and exploring the three-quark potential.

Findings

Complete agreement between theory and simulations in both regimes.

Identification of non-universal constants for correlator comparisons.

Observation of a crossover from elta to Y law in the three-quark potential.

Abstract

We discuss the two- and three-point correlators in the two-dimensional three-state Potts model in the high-temperature phase of the model. By using the form factor approach and perturbed conformal field theory methods we are able to describe both the large distance and the short distance behaviours of the correlators. We compare our predictions with a set of high precision Monte-Carlo simulations (performed on the triangular lattice realization of the model) finding a complete agreement in both regimes. In particular we use the two-point correlators to fix the various non-universal constants involved in the comparison (whose determination is one of the results of our analysis) and then use these constants to compare numerical results and theoretical predictions for the three-point correlator with no free parameter. Our results can be used to shed some light on the behaviour of the three-quark correlator in the confining phase of the (2+1)-dimensional SU(3) lattice gauge theory which is related by dimensional reduction to the three-spin correlator in the high-temperature phase of the three-state Potts model. The picture which emerges is that of a smooth crossover between a \Delta type law at short distances and a Y type law at large distances.