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Journal of Experimental and Theoretical Physics

, Volume 129, Issue 3, pp 421–425 | Cite as

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

  • A. K. Murtazaev
  • M. K. RamazanovEmail author
  • M. K. Mazagaeva
  • M. A. Magomedov
ORDER, DISORDER, AND PHASE TRANSITION IN CONDENSED SYSTEM
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Abstract

Phase transitions and thermodynamic properties of the 2D ferromagnetic Potts model with the number of spin states q = 4 on a hexagonal lattice are investigated by the Mote Carlo method based on the Wang–Landau algorithm. The orders of the phase transitions are investigated using the Binder fourth-order cumulant method and histogram analysis of data. It is established that a first-order transition is observed in the model being investigated.

Notes

FUNDING

This study was supported by the Russian Foundation for Basic Research under research project nos. 19-02-00153-a and 18-32-20098-mod-a-ved.

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 (Amsterdam, Neth.) 476, 1 (2015).Google 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.
    M. K. Ramazanov, A. K. Murtazaev, and M. A. Magomedov, Phys. A (Amsterdam, Neth.) 521, 543 (2019).Google Scholar
  14. 14.
    H. Feldmann, A. J. Guttmann, I. Jensen, R. Shrock, and S.-H. Tsai, J. Phys. A 31, 2287 (1998).ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    A. K. Murtazaev, M. K. Ramazanov, F. A. Kasan-Ogly, and D. R. Kurbanova, J. Exp. Theor. Phys. 120, 110 (2015).ADSCrossRefGoogle Scholar
  16. 16.
    M. K. Badiev, A. K. Murtazaev, and M. K. Ramazanov, J. Exp. Theor. Phys. 123, 623 (2016).ADSCrossRefGoogle Scholar
  17. 17.
    F. Wang and D. P. Landau, Phys. Rev. E 64, 056101 (2001).ADSCrossRefGoogle Scholar
  18. 18.
    F. Wang and D. P. Landau, Phys. Rev. Lett. 86, 2050 (2001).ADSCrossRefGoogle Scholar
  19. 19.
    K. Binder and D. Heermann, Monte Carlo Simulation in Statistical Physics: An Introduction (Springer, Berlin, Heidelberg, 2010).CrossRefGoogle Scholar
  20. 20.
    M. K. Ramazanov and A. K. Murtazaev, JETP Lett. 103, 460 (2016).ADSCrossRefGoogle Scholar
  21. 21.
    M. K. Ramazanov and A. K. Murtazaev, JETP Lett. 106, 86 (2017).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2019

Authors and Affiliations

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

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