### Approximation theory

### Daghestan Electronic Mathematical Reports, Issue 9 (2018)

# Research of the Potts model with $q = 3$ on a triangular lattice by the Wang-Landau algorithm

Magomedov Magomed Alievich, Murtazaev Akai Kurbanovich, Magomedova Liana Kurbanovna, Isaeva Madina Musaevna

### UDK: 537.9

### Pages: 15 - 25

### DOI: 10.31029/demr.9.3

The $q = 3$ Potts model on the triangular lattice with first and second nearest neighbors interaction investigated by the Wang-Landau algorithm of Monte Carlo method. The Density of States of the system and temperature dependence of entropy $S$ are calculated. It is shown that, depending on the ratio of the interactions between the first and second nearest neighbors, the ground state can be both highly degenerate, indicating a frustration in the system, and weakly degenerate. The presence of phase transitions in the system of the first and second order. The phase transition from antiferromagnetic and collinear phases to paramagnetic phase are a phase transition of the first order, whereas the transition from frustrated phase to paramagnetic is a phase transition of the second order. The critical temperature of the phase transitions calculated and phase diagram of the system are determined.

**Keywords: **
Potts model, density of states, triangular lattice, entropy, frustration, phase transition, Monte Carlo method, Wang-Landau algorithm.