Abstract
Based on the Wang--Landau algorithm, the Monte Carlo method was used to study the magnetic structures of the ground state and the thermodynamic properties of the two-dimensional Potts model with the number of spin states q=4 on a triangular lattice, taking into account the exchange interactions of the first J1 and second J2 nearest neighbors. The studies were carried out for the value of the interaction of the second nearest neighbors in the range -2.0≤ J2≤0.0. The magnetic structures of the ground state are constructed in the interval considered. An energy analysis of the magnetic structures of the ground state has been carried out. A phase diagram of the dependence of the critical temperature on the value of J2 is constructed. It is shown that taking into account the interactions of the second nearest neighbors leads to the appearance of frustrations and violation of the magnetic ordering. Keywords: Frustrations, magnetic structures, Monte Carlo method, Potts model.
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