A 3-dimensional Z₃ symmetric model: correlation lengths at a first order phase transition

Abstract

We present a high statistics Monte Carlo investigation of a 3-dimensional Z₃ symmetric model, which is related to SU(3) pure gauge theory at finite temperature. From the finite size scaling behaviour of bulk properties and the existence of metastable states, we conclude that this model exhibits a first-order phase transition. We have also performed detailed correlation length measurements in a cylindrical geometry with periodic boundary conditions as well as with cold walls in the longitudinal direction. The correlation length, which appears to be independent of the boundary conditions, becomes very large near the critical point. Nonetheless, our data suggest that the correlation length develops a discontinuity at the critical point in the infinite volume limit.