Mean-Field Analysis of Antiferromagnetic Three-State Potts Model with Next Nearest Neighbor Interaction

Abstract

The three-state Potts model with antiferromagnetic nearest-neighbor (n.n.) and ferromagnetic next-nearest-neighbor (n.n.n) interaction is investigated within a mean-field theory. We find that the phase-diagram contains two kind of ordered phases, so-called BSS phase and PSS phase, separated by a discontinuous phase transition line. Order-disorder transition is continuous for the weak n.n.n. interaction and becomes discontinuous transition when the n.n.n. interaction is increased. We show that the multicritical point where the order-disorder transition becomes discontinuous is indeed a tricritical point.