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Physics of the Solid State

, Volume 61, Issue 11, pp 2172–2176 | Cite as

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

  • A. K. Murtazaev
  • D. R. KurbanovaEmail author
  • M. K. Ramazanov
LATTICE DYNAMICS
  • 3 Downloads

Abstract

The phase transitions and the thermodynamic properties of the two-dimensional ferromagnetic Potts model with the number of spin states q = 4 on a triangular lattice are studied on the base of the Wang–Landau algorithm of the Monte Carlo method. The phase transition characters are analyzed using the method of the four-order Binder cumulants and the histogram analysis of the data. It is found that a first-order phase transition is observed in the model under study.

Keywords:

phase transitions critical phenomena Potts model Monte Carlo method 

Notes

FUNDING

This work was supported by the Russian foundation for Basic Research, project no. 18-32-00391-mol-a.

CONFLICT OF INTEREST

The authors declare that they have no conflicts of interest.

REFERENCES

  1. 1.
    H. T. Diep, Frustrated Spin Systems (World Scientific, Singapore, 2004).zbMATHGoogle Scholar
  2. 2.
    R. J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic, New York, 1982; Mir, Moscow, 1985).Google Scholar
  3. 3.
    F. Y. Wu, Exactly Solved Models: A Journey in Statistical Mechanics (World Scientific, New Jersey, 2008).Google Scholar
  4. 4.
    F. Y. Wu, Rev. Mod. Phys. 54, 235 (1982).ADSCrossRefGoogle Scholar
  5. 5.
    W. Zhang and Y. Deng, Phys. Rev. E 78, 031103 (2008).ADSCrossRefGoogle Scholar
  6. 6.
    A. K. Murtazaev, M. K. Ramazanov, F. A. Kassan-Ogly, and M. K. Badiev, J. Exp. Theor. Phys. 117, 1091 (2013).CrossRefGoogle Scholar
  7. 7.
    A. K. Murtazaev, M. K. Ramazanov, and M. K. Badiev, Phys. B: Condens. Matter 476, 1 (2015).ADSCrossRefGoogle Scholar
  8. 8.
    F. A. Kassan-Ogly, A. K. Murtazaev, A. K. Zhuravlev, M. K. Ramazanov, and A. I. Proshkin, J. Magn. Magn. Mater. 384, 247 (2015).ADSCrossRefGoogle Scholar
  9. 9.
    M. K. Ramazanov, A. K. Murtazaev, and M. A. Magomedov, Solid State Commun. 233, 35 (2016).ADSCrossRefGoogle Scholar
  10. 10.
    M. K. Ramazanov, A. K. Murtazaev, M. A. Magomedov, and M. K. Badiev, Phase Trans. 91, 610 (2018).CrossRefGoogle Scholar
  11. 11.
    M. Nauenberg and D. J. Scalapino, Phys. Rev. Lett. 44, 837 (1980).ADSCrossRefGoogle Scholar
  12. 12.
    J. L. Cardy, M. Nauenberg, and D. J. Scalapino, Phys. Rev. B 22, 2560 (1980).ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    F. Y. Wu, Rev. Mod. Phys. 54, 235 (1982).ADSCrossRefGoogle Scholar
  14. 14.
    M. K. Ramazanov, A. K. Murtazaev, and M. A. Magomedov, Phys. A (Amsterdam, Neth.) 521, 543 (2019).Google Scholar
  15. 15.
    H. Feldmann, A. J. Guttmann, I. Jensen, R. Shrock, and S.-H. Tsai, J. Phys. A 31, 2287 (1998).ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    A. K. Murtazaev, M. K. Ramazanov, F. A. Kasan-Ogly, and D. R. Kurbanova, J. Exp. Theor. Phys. 120, 110 (2015).ADSCrossRefGoogle Scholar
  17. 17.
    A. K. Murtazaev, M. K. Ramazanov, M. A. Magomedov, and D. R. Kurbanova, Phys. Solid State 60, 1848 (2018).ADSCrossRefGoogle Scholar
  18. 18.
    A. K. Murtazaev, M. K. Ramazanov, D. R. Kurbanova, M. A. Magomedov, and K. Sh. Murtazaev, Mater. Lett. 236, 669 (2019).CrossRefGoogle Scholar
  19. 19.
    F. Wang and D. P. Landau, Phys. Rev. E 64, 056101 (2001).ADSCrossRefGoogle Scholar
  20. 20.
    F. Wang and D. P. Landau, Phys. Rev. Lett. 86, 2050 (2001).ADSCrossRefGoogle Scholar
  21. 21.
    Monte Carlo Methods in Statistical Physics, Ed. by K. Binder (Springer, Berlin, 1979).Google Scholar
  22. 22.
    A. M. Ferrenberg and R. H. Swendsen, Phys. Rev. Lett. 61, 2635 (1988).ADSCrossRefGoogle Scholar
  23. 23.
    A. M. Ferrenberg and R. H. Swendsen, Phys. Rev. Lett. 63, 1195 (1989).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  • A. K. Murtazaev
    • 1
  • D. R. Kurbanova
    • 1
    Email author
  • M. K. Ramazanov
    • 1
  1. 1.Institute of Physics, Dagestan Scientific Center, Russian Academy of SciencesMakhachkalaRussia

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