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Diffusion and defect data, solid state data. Part B, Solid state phenomena/Solid state phenomena

The Investigation of Phase Transitions in Two-Dimensional 3-State Antiferromagnetic Potts Model on a Triangular Lattice with Interaction of Next Nearest Neighbors

Akai Kurbanovich Murtazaev, Albert Babaevich Babaev, Felix A. Kassan-Ogly

Published Apr 1, 2014• 4 citations
Publisher

Abstract

The phase transitions and critical phenomena in two-dimensional 3-state antiferromagnetic Potts model with account of next-nearest neighbors are investigated by Monte-Carlo method. The systems with linear sizesL=20-144 are explored. Following parities of exchange interactions are considered. Moreover, we analyze the character of phase transitions and determine the critical temperatures.

DOI
10.4028/www.scientific.net/ssp.215.52

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We have studied phase transitions and thermodynamic properties of the antiferromagnetic Potts model with number of spin states q = 3 on a body-centered cubic lattice by the Monte Carlo method. Investigations have been performed with account for exchange interactions J1 and J2 between the first and second nearest neighbors. The phase transition order has been analyzed using the histogram method. It is found that in this model with J2 = 0, a second-order phase transition is observed. It is concluded that the inclusion of the interaction between the second nearest neighbors changes the type of the phase transition.
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Abstract The Monte Carlo method has been used to study phase transitions and critical properties of the antiferromagnetic 3-state Potts model on a body-centered cubic lattice with interactions of the first (J1) and second (J2) nearest neighbors. The competition of exchange interactions in the range –2/3 < J2 < 0 was determined to result in a phase separation. In the low-temperature region, an ordered phase, lying inside the phase with broken sublattice symmetry, was found. The magnetic structures of the ground state corresponding to different regions of the phase diagram have been obtained. The analysis of the phase transition order has been carried out using the Binder cumulant method and the histogram method. It has been revealed that the interaction of the second nearest neighbors leads to a change in the type of phase transition. Static critical exponents have been calculated based on scaling relations. The critical exponents correspond to the universality class of the three-dimensional XY model.
Based on the replica algorithm by the Monte Carlo method, a computer simulation of the three-dimensional antiferromagnetic Heisenberg model is performed, taking into account the interactions of the first and second nearest neighbors. The phase transitions of this model are studied. The investigations were carried out for the ratios of the exchange interactions of the first and second nearest neighbors r=J2/J1r = J_2 / J_1r=J2​/J1​ in the range 0.0≤r≤1.00.0 \leq r \leq 1.00.0≤r≤1.0. The phase diagram of the critical temperature dependence on a value of the next-nearest neighbor interaction is plotted.