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Frustrations and phase transitions in the three-vertex Potts model with next-nearest-neighbor interactions on a triangular lattice

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Abstract

Phase transitions in two-dimensional arrays described by the three-vertex Potts model involving the interactions between magnetic moments located at the nearest-neighbor and next-nearest-neighbor sites of a triangular lattice are studied using the Monte Carlo method. The ratio of the next-nearest-neighbor and nearest-neighbor exchange constants r = J 2/J 1 is chosen within the 0–1 range. The analysis of the low temperature behavior of the entropy and density of states in the system, as well as of the fourth-order Binder cumulants, shows that in the range 0 ≤ r < 0.2, this model exhibits a first-order phase transition, whereas at r ≥ 0.2, frustrations arise in such a system.

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Authors and Affiliations

  1. Amirkhanov Institute of Physics, Dagestan Scientific Center, Russian Academy of Sciences, ul. Yaragskogo 94, Makhachkala, 367003, Russia

    A. K. Murtazaev, A. B. Babaev & M. A. Magomedov

  2. Dagestan State University, ul. Gadzhieva 43a, Makhachkala, 367025, Russia

    A. K. Murtazaev & M. A. Magomedov

  3. Dagestan State Pedagogical University, ul. Yaragskogo 57, Makhachkala, 367003, Russia

    A. B. Babaev

  4. Institute of Metal Physics, Ural Branch, Russian Academy of Sciences, ul. S. Kovalevskoi 18, Yekaterinburg, 620990, Russia

    F. A. Kassan-Ogly & A. I. Proshkin

Authors
  1. A. K. Murtazaev
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  2. A. B. Babaev
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  3. M. A. Magomedov
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  4. F. A. Kassan-Ogly
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  5. A. I. Proshkin
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Correspondence to A. B. Babaev.

Additional information

Original Russian Text © A.K. Murtazaev, A.B. Babaev, M.A. Magomedov, F.A. Kassan-Ogly, A.I. Proshkin, 2014, published in Pis’ma v Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2014, Vol. 100, No. 4, pp. 267–271.

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Murtazaev, A.K., Babaev, A.B., Magomedov, M.A. et al. Frustrations and phase transitions in the three-vertex Potts model with next-nearest-neighbor interactions on a triangular lattice. Jetp Lett. 100, 242–246 (2014). https://doi.org/10.1134/S0021364014160115

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  • DOI: https://doi.org/10.1134/S0021364014160115

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