Three-state Potts model on triangular lattice with nearest-neighbor and next-nearest-neighbor antiferromagnetic interactions

Using Monte Carlo simulations, we investigated phase transitions and frustrations in the three-state Potts model on a triangular lattice with allowance for antiferromagnetic exchange interactions between nearest-neighbors J(1) and next-nearest-neighbors J(2). The ratio of the next-nearest-neighbor and nearest neighbor exchange constants r=J(2)/J(1) is chosen within the range of 0 <= r <= 2. Based on the analysis of the entropy, specific heat, system state density function, and fourth order Binder cumulants, the phase transitions in the Potts model with interactionsh J(1) < 0 and J(2) < 0 are shown to be found in value ranges of 0 <= r < 0.2 and 1.25 <= r <= 2.0. In an intermediate range of 0.2 <= r <= 1.0 the phase transition fails and the frustrations are revealed. (C) 2016 Elsevier Ltd. All rights reserved.