Potts correlators and the static 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 Δtype law at short distances and a Y type law at large distances.

38 pages, 13 eps figures, LaTeX

References in corpus (7)

• Detailed Analysis of the Three Quark Potential in SU(3) Lattice QCD
• String excitation energies in SU(N) gauge theories beyond the free-string approximation
• The ground state of three quarks
• String effects in the 3d gauge Ising model
• The baryon static potential from lattice QCD
• Polyakov loop correlators from D0-brane interactions in bosonic string theory
• Exact Potts Model Partition Functions for Strips of the Triangular Lattice

Cited by in corpus (8)

• The S-matrix Bootstrap IV: Multiple Amplitudes
• On the intrinsic width of the chromoelectric flux tube in finite temperature LGTs
• Precise determination of the three-quark potential in SU(3) lattice gauge theory
• The three-dimensional, three state Potts model in a negative external field
• Asymptotic scattering and duality in the one-dimensional three-state quantum Potts model on a lattice
• Three-quark potentials in an $SU(3)$ effective Polyakov loop model
• Form Factors of the Tricritical Three-state Potts Model in its Scaling Limit
• Rate of cluster decomposition via Fermat-Steiner point