Phase transitions in the frustrated Potts model in the magnetic field

Abstract

The influence of the magnetic field on phase transitions, magnetic and thermodynamic properties of the two-dimensional Potts model with q = 4 on a hexagonal lattice with the nearest and next-nearest neighbors interactions is studied using the replica algorithm of the Monte Carlo method . The studies are carried out in the magnetic field range −1.0 ≤ h ≤ 7.0 with a step of 0.1. A phase diagram of the magnetization dependence on magnetic field value is plotted. It is found that a first-order phase transition is observed in the ranges 0.0 ≤ h ≤ 1.0 and 2.0 ≤ h ≤ 3.5. A second-order phase transition is observed for the magnetic field value h = 1.5. It is revealed that there is no the ground-state degeneracy and the phase transition is smeared for magnetic field values of h ≥ 4.0. A phase diagram of the dependence of the critical temperature on the magnitude of the interaction of the next-nearest neighbors is constructed. • A two-dimensional frustrated Potts model are investigated. • The magnetic structures of the ground-state for considered model are obtained. • The phase diagram is plotted. • It is shown that magnetic fields destroyed the phase transition.