Phase diagram of the four-vertex Potts model with competing exchange interactions

Phase transitions and magnetic structures in the ground state of the two-dimensional Potts model with four spin states on a triangular lattice with competing exchange interactions of the first, $J_1$, and second, $J_2$, nearest neighbors have been studied using the Wang–Landau Monte Carlo algorithm. The phase diagram of the critical temperature versus $J_2$ has been obtained. It has been revealed that the transition from the ferromagnetic phase to the paramagnetic one is a second-order phase transition, whereas the transition from the stripe and stripe–triplet phases to the paramagnetic one is a first-order phase transition. The magnetic structures of the ground state corresponding to different regions of the phase diagram have been determined. It has been found that the competition between exchange interactions in the range of $ - 1.2 \leqslant J_2 \leqslant - 0.9$ leads to strong frustration and breaking of magnetic order.