Computer simulation of phase transitions in low-dimensional Potts models

The Monte Carlo method is used to study phase transitions in the two-dimensional Potts model with the number of states spin $q=3$ on square and hexagonal lattices. Considered systems with linear dimensions $L\times L=N$, $L = 21\div102$. The obtained numerical data indicate that in the considered In the Potts model, a second-order phase transition is observed in accordance with the analytical theory. The Binder cumulants method of the fourth order determines the values of the critical points of the Potts model on different lattices.