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Journal of Experimental and Theoretical Physics

Phase Transitions and Thermodynamic Properties of the Potts Model with Spin States Number q = 4 on a Hexagonal Lattice

Akai Kurbanovich Murtazaev, Рамазанов Магомедшейх Курбанович, M. K. Mazagaeva, М. А. Магомедов

Published Sep 1, 2019• 21 citations
Publisher

Abstract

Abstract Phase transitions and thermodynamic properties of the 2D ferromagnetic Potts model with the number of spin states q = 4 on a hexagonal lattice are investigated by the Mote Carlo method based on the Wang–Landau algorithm. The orders of the phase transitions are investigated using the Binder fourth-order cumulant method and histogram analysis of data. It is established that a first-order transition is observed in the model being investigated.

DOI
10.1134/s1063776119080053

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Abstract Phase transitions and thermodynamic properties of the 2D ferromagnetic Potts model with the number of spin states q = 4 on a hexagonal lattice are investigated by the Mote Carlo method based on the Wang–Landau algorithm. The orders of the phase transitions are investigated using the Binder fourth-order cumulant method and histogram analysis of data. It is established that a first-order transition is observed in the model being investigated.
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Abstract The Wang–Landau algorithm of the Monte Carlo method is used to study the magnetic structures of the ground state, phase transitions, and thermodynamic properties of the two-dimensional antiferromagnetic Potts model with number q = 4 of spin states in a hexagonal lattice with the interactions of the nearest (J1) and next-to-nearest (J2) neighbors. The exchange interaction ratios in the range of 0.0 ≤ r = |J2/J1| ≤ 1.0 are studied. A phase diagram of the dependence of the critical temperature on the exchange interaction value of the next-to-nearest neighbors is constructed. The nature of phase transitions is analyzed. It is found that a first-order phase transition is observed in the range of 0.1 ≤ r ≤ 1.0, while there is no phase transition in the system and a strong degeneracy of the ground state is observed at r = 0.0.
The Monte Carlo method is used to study phase transitions in a two-dimensional weakly diluted 4-state Potts model on a hexagonal lattice. Systems with linear dimensions L=21/336 at spin concentrations p=1.00, 0.90 are considered. The use of the fourth-order binder cumulants method and histogram data analysis showed that the introduction of nonmagnetic impurities has a stabilizing role in the implementation of the second-order phase transition in the Potts model under study on a hexagonal lattice. Keywords: Potts model, Monte Carlo method, thermodynamic parameters, disorder.