Phase transformations and thermodynamic properties of the Potts model with $q$ = 4 on a hexagonal lattice with interactions of next-nearest neighbors

Magnetic structures of the ground state, phase transitions and thermodynamic properties of the 2D ferromagnetic Potts model with the number of spin states $q$ = 4 on a hexagonal lattice with next-nearest neighbors interactions are investigated by the Monte Carlo method based on the Wang–Landau algorithm. It is shown that taking into account the antiferromagnetic interactions of the next-nearest neighbors leads to the appearance of frustration and a violation of magnetic ordering. The orders of the phase transitions are investigated using the Binder fourth-order cumulant method and histogram analysis of data. It is established that a first-order transition is observed in the model being investigated.