Phase transitions and thermodynamic properties of the 2D ferromagnetic Potts model with the number of spin states q = 4 on a kagome lattice are investigated by the Mote Carlo method based on the Wang-Landau algorithm. 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.

The phase transitions and thermodynamic properties of the two-dimensional antiferromagnetic Potts model with the number of spin states q = 4 on the kagome lattice are studied by the Monte Carlo method, 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 interval -1.0 ≤ J2 ≤ 0.0. An analysis of the character of phase transitions has been carried out. It is shown that in the interval -1.0 ≤ J2 ≤ -0.1, a second-order phase transition is observed, while at J2 = 0.0, frustrations disturb the order in the system and lead to the disappearance of the phase transition.