Absence of Z 3 criticality in a three-dimensional Potts model with extended couplings

Abstract

The order-disorder phase transition has been reported to be of second order in the three-dimensional three-state Potts model with ferromagnetic nearest-neighbor ( J 1) and antiferromagnetic next-to-nearest-neighbor ( J 2) couplings. This contradicts the conventional picture in which Z 3 criticality does not exist in three dimensions and has been proposed as a concrete example of the “fluctuation-induced second-order phase transition” of Fucito and Parisi. Monte Carlo calculations on 32 3 and 64 3 lattices (for J 2 J 1=−0.1 and −0.2 ) demonstrate, however, that this phase transition is of first order, in keeping with conventional expectations.