COMPUTER SIMULATION OF ANTIFERROMAGNETIC STRUCTURES DESCRIBED BY THE THREE-VERTEX ANTIFERROMAGNETIC POTTS MODEL

Abstract

Abstract. Objectives A computer simulation of the antiferromagnetic structures described by the three-vertex Potts model on a triangular lattice is performed, taking into account the antiferromagnetic exchange interactions between the nearest J1 and second J2 neighbours. The main goal of the computer simulation was to elucidate the effects of ground state and areas of frustration on the thermodynamic and magnetic properties of antiferromagnetic structures described by the lowdimensional Potts model. Method The computer simulation is based on the Monte Carlo method. This method is implemented using the Metropolis algorithm in combination with the Wolff claster algorithm. The computer simulation was carried out for low-dimensional systems with periodic boundary conditions and linear dimensions L = 24124. Results On the basis of heat capacity and entropy analysis, phase transitions were observed in the considered model to possess exchange interaction parameters J1 <0 and J2 <0 in the variation intervals 0r<0.2 and 1.0<r2.0 (r=J2/J1). In the intermediate interval 0,2r1,0 there is no phase transition, and frustrations are observed. The temperature dependences of thermodynamic parameters, such as heat capacity, susceptibility and entropy, were obtained for all considered systems with linear dimensions L. The behaviour of these parameters, both at low and high temperatures, is discussed. The temperatures of the phase transitions are determined using the Binder fourth-order cumulant method. Conclusion Cases are shown in which, depending on the r-value, either a phase transition or a frustration is observed in the simulated system. It is proved that the competition between the exchange parameters of the first and second nearest neighbors in the r variation interval 0,2r1,0 leads to a degeneracy in the examined structure ground state; frustrations are additionally observed in the interval under consideration. On the basis of the obtained data, a phase diagram is constructed depending on the phase transition temperature and r-ratio.

Keywords

• frustrations
• phase transitions
• potts model
• triangular lattice