Phase transitions and the magnetic properties of the Potts model with four spin states on a hexagonal lattice in low magnetic fields

Phase transitions and the magnetic properties of the two-dimensional Potts model with the four spin states on a hexagonal lattice in low magnetic fields are studied using the replica exchange algorithm of the Monte Carlo method. The studies are performed in the magnetic field range of $0.0 \leqslant H \leqslant 3.5$ with a step of $0.5$. For this $H$ range, the magnetic structures of the ground state are determined. It is found that the first-order phase transition occurs in the whole magnetic field range under study, except for $H = 1.5$, at which the second-order phase transition takes place. In the framework of such model, it is demonstrated that the applied magnetic field can lead to a change in the order of the phase transition.