The correlation lengths and the order of the phase transition in three-dimensional Z₃ symmetric models

Abstract

We present a high statistics Monte Carlo investigation of three-dimensional Z₃ symmetric models, which are 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 these models exhibit 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 a cold wall 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 developes a discontinuity at the critical point in the infinite volume limit.