A.B. Babaev - Ph.D. (Phys.-Math.), Associate Professor, Institute of Physics, Dagestan Scientific Center, Russian Academy of Sciences (Makhachkala) Е-mail: b_albert78@mail.ru A.K. Murtazaev - Dr.Sc. (Phys.-Math.), Professor, Corresponding Member RAS, Director of Institute of Physics, Dagestan Scientific Center, Russian Academy of Sciences (Makhachkala) E-mail: m_akai2005@mail.ru T.R. Rizvanova - Post-graduate Student, Institute of Physics, Dagestan Scientific Center, Russian Academy of Sciences (Makhachkala) Е-mail: b_albert78@mail.ru

Phase transitions, frustrations and magnetic ordering in two-dimensional structures described by a three-vertex antiferromagnetic Potts model on a triangular lattice are investigated by the Monte Carlo method with regard to nearest and next-nearest neighbors with interaction constants J1 and J2, respectively. Phase transitions in these models are analyzed for the ratio r = J2/J1 of next-nearest to nearest exchange interaction constants in the interval 0 ≤ r ≤ 2,0. On the basis of the analysis of the low-temperature entropy, and the fourth-order Binder cumulants, it is shown that a Potts model with interaction constants J1 < 0 and J2 < 0 exhibits a first-order Phase transitions in the range of 0≤ r < 0,2 and 1,0 < r ≤ 2,0, whereas, in the interval 0,2 ≤ r ≤ 1,0, frustrations arise in the system.

 

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