Thermodynamic and magnetic properties of a three-state Potts model on a triangular lattice with next-neighbor interactions

Using Monte Carlo calculations, we study the thermodynamic and magnetic properties of 2D structures that can be described by a three-state Potts model on a triangular lattice with nearest- and secondnearest- neighbor interactions characterized by the coupling constants $J_{1}$ and $J_{2}$, respectively. Analyzing the thermodynamic parameters of heat capacity, the order parameter, the susceptibility, and fourth-order Binder cumulants, we show that the three-state Potts model with coupling constants $J_{1}>$ 0 and $J_{2}<$ 0 predicts a phase transition of the second kind for 0 $\le |r|\le$ 1/3, where $r=J_{2}/J_{1}$.