Influence of magnetic field on phase transitions in the antiferromagnetic Potts model

Based on the replica exchange algorithm of the Monte Carlo method, the influence of an external magnetic field on phase transitions and thermodynamic properties of the two-dimensional antiferromagnetic Potts model with the number of spin states q = 4 on a hexagonal lattice was studied. The studies were conducted in the range of external magnetic field values of 0.0 ≤ h ≤ 10.0. The magnetic field is measured in relative units of exchange interaction between nearest neighbors |J1|. The magnetic structures of the ground state were obtained, and the nature of phase transitions in the considered field range was analyzed. It has been established that in the intervals 0.0 ≤ h ≤ 3.0 and 6.0 ≤ h ≤ 6.5 a first-order phase transition is observed. It is shown that at the external magnetic field values h = 3.5 and 5.5, the system is frustrated, and in the magnetic field intervals 4.0 ≤ h ≤ 5.0 and 7.0 ≤ h ≤ 8.5, the system approaches the frustration regime. It was found that strong magnetic fields (h ≥ 9.0) suppress the phase transition in the system.