A study of the correlation length near a first-order phase transition: the three-dimensional three-state potts model

Abstract

A high statistics study of the 3-d three-state Potts model on lattices of size L³, with L ranging from 12 to 48, confirms the first-order nature of the Z(3) symmetry breaking phase transition in this model. We investigate the behaviour of spin-spin correlations in the critical region, comment on various methods to extract the correlation lengths and point out the resulting ambiguities on finite lattices. Our results indicate a finite correlation length at β_c. However, a careful analysis of the correlation functions is necessary to disentangle the inverse mass gap from the tunnelling correlation length which we found to diverge as L at β_c although the transition is clearly first order.