Renormalization group study of the three state three dimensional Potts model

Abstract

We make a renormalisation group study with the finite size real space renormalization group (FSRSRG) technique of the order of the transition in the three dimensional three state Potts model with nearest neighbor and next to nearest neighbour couplings. Our results provide evidence that the order-disorder transition from a high temperature phase to a low temperature phase is discontinuous not only in the region characterized by both couplings being positive but also when the next to nearest coupling is appreciably antiferromagnetic. In both cases the correlation length exponent, previously not known, converges to the value expected for a first order first transition but only for large volumes, especially in the antiferromagnetic case.