Phase transitions in a two-dimensional antiferromagnetic Potts model on a triangular lattice with next-nearest neighbor interactions

doi:https://doi.org/10.1134/S1063776116020163

Title: Phase transitions in a two-dimensional antiferromagnetic Potts model on a triangular lattice with next-nearest neighbor interactions

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Abstract

Phase transitions (PTs) and frustrations 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 J{sub 1} and J{sub 2}, respectively. PTs in these models are analyzed for the ratio r = J{sub 2}/J{sub 1} of next-nearest to nearest exchange interaction constants in the interval |r| = 0–1.0. On the basis of the analysis of the low-temperature entropy, the density of states function of the system, and the fourth-order Binder cumulants, it is shown that a Potts model with interaction constants J{sub 1} < 0 and J{sub 2} < 0 exhibits a first-order PT in the range of 0 ⩽ r < 0.2, whereas, in the interval 0.2 ⩽ r ⩽ 1.0, frustrations arise in the system. At the same time, for J{sub 1} > 0 and J{sub 2} < 0, frustrations arise in the range 0.5 < |r| < 1.0, while, in the interval 0 ⩽ |r| ⩽ 1/3, the model exhibits a second-order PT.

Authors:

Magomedov, M. A.; Murtazaev, A. K. ^[1]; Kassan-Ogly, F. A.; Proshkin, A. I. ^[2]

Russian Academy of Sciences, Amirkhanov Institute of Physics, Dagestan Scientific Center (Russian Federation)
Russian Academy of Sciences, Institute of Metal Physics, Ural Branch (Russian Federation)

Publication Date:: 2016-02-15

OSTI Identifier:: 22617354

Resource Type:: Journal Article

Journal Name:: Journal of Experimental and Theoretical Physics

Additional Journal Information:: Journal Volume: 122; Journal Issue: 2; Other Information: Copyright (c) 2016 Pleiades Publishing, Inc.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1063-7761

Country of Publication:: United States

Language:: English

Subject:: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; ANTIFERROMAGNETISM; BINDERS; DENSITY OF STATES; ENTROPY; EXCHANGE INTERACTIONS; MONTE CARLO METHOD; PHASE TRANSFORMATIONS; SIMULATION; TRIANGULAR CONFIGURATION; TWO-DIMENSIONAL CALCULATIONS; TWO-DIMENSIONAL SYSTEMS

Citation Formats


                    Babaev, A. B., E-mail: b-albert78@mail.ru, Magomedov, M. A., Murtazaev, A. K., Kassan-Ogly, F. A., and Proshkin, A. I. Phase transitions in a two-dimensional antiferromagnetic Potts model on a triangular lattice with next-nearest neighbor interactions.  United States: N. p., 2016. 
        Web.  doi:10.1134/S1063776116020163.

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                    Babaev, A. B., E-mail: b-albert78@mail.ru, Magomedov, M. A., Murtazaev, A. K., Kassan-Ogly, F. A., & Proshkin, A. I. Phase transitions in a two-dimensional antiferromagnetic Potts model on a triangular lattice with next-nearest neighbor interactions.  United States.  https://doi.org/10.1134/S1063776116020163

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                    Babaev, A. B., E-mail: b-albert78@mail.ru, Magomedov, M. A., Murtazaev, A. K., Kassan-Ogly, F. A., and Proshkin, A. I. Mon .  
        "Phase transitions in a two-dimensional antiferromagnetic Potts model on a triangular lattice with next-nearest neighbor interactions".  United States.  https://doi.org/10.1134/S1063776116020163.

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@article{osti_22617354,

  title        = {Phase transitions in a two-dimensional antiferromagnetic Potts model on a triangular lattice with next-nearest neighbor interactions},

  author       = {Babaev, A. B., E-mail: b-albert78@mail.ru and Magomedov, M. A. and Murtazaev, A. K. and Kassan-Ogly, F. A. and Proshkin, A. I.},

  abstractNote = {Phase transitions (PTs) and frustrations 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 J{sub 1} and J{sub 2}, respectively. PTs in these models are analyzed for the ratio r = J{sub 2}/J{sub 1} of next-nearest to nearest exchange interaction constants in the interval |r| = 0–1.0. On the basis of the analysis of the low-temperature entropy, the density of states function of the system, and the fourth-order Binder cumulants, it is shown that a Potts model with interaction constants J{sub 1} < 0 and J{sub 2} < 0 exhibits a first-order PT in the range of 0 ⩽ r < 0.2, whereas, in the interval 0.2 ⩽ r ⩽ 1.0, frustrations arise in the system. At the same time, for J{sub 1} > 0 and J{sub 2} < 0, frustrations arise in the range 0.5 < |r| < 1.0, while, in the interval 0 ⩽ |r| ⩽ 1/3, the model exhibits a second-order PT.},

  doi          = {10.1134/S1063776116020163},

  url          = {https://www.osti.gov/biblio/22617354},
  journal      = {Journal of Experimental and Theoretical Physics},

  issn         = {1063-7761},

  number       = 2,

  volume       = 122,

  place        = {United States},

  year         = {2016},

  month        = {2}

}

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