Potts correlators and the static three-quark potential

Abstract

We discuss the two- and three-point correlators in the two-dimensional three-state Pottsmodel in the high temperature phase of the model. By using the form factor approach andperturbed conformal field theory methods we are able to describe both the large distanceand the short distance behaviours of the correlators. We compare our predictions with a setof high precision Monte Carlo simulations (performed on the triangular lattice realizationof the model) finding a complete agreement in both regimes. In particular we use thetwo-point correlators to fix the various non-universal constants involved in thecomparison (whose determination is one of the results of our analysis) and then usethese constants to compare numerical results and theoretical predictions for thethree-point correlator with no free parameter. Our results can be used to shed somelight 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 correlatorin the high temperature phase of the three-state Potts model. The picture which emerges isthat of a smooth crossover between a Δ-type law at short distances and aY-type law at large distances.