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Phase Transitions and the Thermodynamic Properties of the Potts Model with the Spin State Number q = 4 at a Kagome Lattice

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Abstract

Phase transitions and the thermodynamic properties of the two-dimensional ferromagnetic Izing model with spin state number q = 4 on a kagome lattice are studied by the Monte Carlo method on the base of the Wang–Landau algorithm. The phase transition character is analyzed using the fourth-order Binder cumulant method and the histogram analysis of the data. It is found that this model undergoes a first-order phase transition.

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REFERENCES

  1. H. T. Diep, Frustrated Spin Systems (World Scientific, Singapore, 2004).

    MATH  Google Scholar 

  2. R. J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic, New York, 1982).

    MATH  Google Scholar 

  3. F. Y. Wu, Exactly Solved Models: A Journey in Statistical Mechanics (World Scientific, N. J., 2008).

    Google Scholar 

  4. F. Y. Wu, Rev. Mod. Phys. 54, 235 (1982).

    Article  ADS  Google Scholar 

  5. W. Zhang and Y. Deng, Phys. Rev. E 78, 031103 (2008).

    Article  ADS  Google Scholar 

  6. A. Nakano, M. E. Bachlechner, R. K. Kalia, F. Lidorikis, P. Vashishta, G. Z. Voyiadjis, T. J. Campbell, S. Ogata, and F. Shimojo, Comput. Sci. Eng. 3, 56 (2001).

    Article  Google Scholar 

  7. T. Fabritius, N. Laflorencie, and S. Wessel, Phys. Rev. B 82, 035402 (2010).

    Article  ADS  Google Scholar 

  8. R. Masrour, L. Bahmad, and A. Benyoussef, J. Magn. Magn. Mater. 324, 3991 (2012).

    Article  ADS  Google Scholar 

  9. N. Schreiber, R. Cohen, and S. Haber, Phys. Rev. E 97, 032106 (2018).

    Article  ADS  MathSciNet  Google Scholar 

  10. D. P. Foster and C. Gérard, Phys. Rev. B 70, 014411 (2004).

    Article  ADS  Google Scholar 

  11. I. Puha and H. T. Diep, J. Appl. Phys. 87, 5905 (2000).

    Article  ADS  Google Scholar 

  12. M. Nauenberg and D. J. Scalapino, Phys. Rev. Lett. 44, 837 (1980).

    Article  ADS  Google Scholar 

  13. J. L. Cardy, M. Nauenberg, and D. J. Scalapino, Phys. Rev. B 22, 2560 (1980).

    Article  ADS  MathSciNet  Google Scholar 

  14. M. K. Ramazanov, A. K. Murtazaev, and M. A. Magomedov, Phys. A (Amsterdam, Neth.) 521, 543 (2019).

  15. S. Ostlund, Phys. Rev. B 24, 398 (1981).

    Article  ADS  MathSciNet  Google Scholar 

  16. M. Quartin and S. L. A. de Queiroz, J. Phys. A 36, 951 (2003).

    Article  ADS  MathSciNet  Google Scholar 

  17. D. P. Foster and C. Gérard, J. Phys. A 35, L75 (2002).

    Article  ADS  Google Scholar 

  18. H. Feldmann, A. J. Guttmann, I. Jensen, R. Shrock, and S.-H. Tsai, J. Phys. A 31, 2287 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  19. M. Nauenberg and D. J. Scalapino, Phys. Rev. Lett. 44, 837 (1980).

    Article  ADS  Google Scholar 

  20. J. L. Cardy, M. Nauenberg, and D. J. Scalapino, Phys. Rev. B 22, 2560 (1980).

    Article  ADS  MathSciNet  Google Scholar 

  21. A. K. Murtazaev, D. R. Kurbanova, and M. K. Ramazanov, Phys. Solid State 61, 2172 (2019).

    Article  ADS  Google Scholar 

  22. A. K. Murtazaev, M. K. Ramazanov, M. K. Mazagaeva, and M. A. Magomedov, J. Exp. Theor. Phys. 129, 421 (2019).

    Article  ADS  Google Scholar 

  23. M. K. Ramazanov, A. K. Murtazaev, M. A. Magomedov, and M. K. Mazagaeva, Phys. Solid State 62, 499 (2020).

    Article  ADS  Google Scholar 

  24. M. K. Ramazanov and A. K. Murtazaev, JETP Lett. 103, 460 (2016).

    Article  ADS  Google Scholar 

  25. M. K. Ramazanov and A. K. Murtazaev, JETP Lett. 106, 86 (2017).

    Article  ADS  Google Scholar 

  26. A. K. Murtazaev, M. A. Magomedov, and M. K. Ramazanov, JETP Lett. 107, 259 (2018).

    Article  ADS  Google Scholar 

  27. M. K. Ramazanov and A. K. Murtazaev, J. Exp. Theor. Phys. 109, 589 (2019).

    Article  Google Scholar 

  28. A. K. Murtazaev, M. K. Ramazanov, K. Sh. Murtazaev, M. A. Magomedov, and M. K. Badiev, Phys. Solid State 62, 273 (2020).

    Article  ADS  Google Scholar 

  29. F. Wang and D. P. Landau, Phys. Rev. E 64, 056101 (2001).

    Article  ADS  Google Scholar 

  30. F. Wang and D. P. Landau, Phys. Rev. Lett. 86, 2050 (2001).

    Article  ADS  Google Scholar 

  31. K. Binder and D. W. Heermann, Monte Carlo Simulation in Statistical Physics (Springer, Berlin, 1988), p. 214.

    Book  Google Scholar 

  32. A. K. Murtazaev, D. R. Kurbanova, and M. K. Ramazanov, J. Exp. Theor. Phys. 129, 903 (2019).

    Article  ADS  Google Scholar 

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Funding

This study was supported by the Russian Foundation for Basic Research, project no. 19-02-00153-a.

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Authors and Affiliations

  1. Institute of Physics, Dagestan Federal Scientific Center, Russian Academy of Sciences, 367015, Makhachkala, Russia

    A. K. Murtazaev, T. R. Rizvanova, M. K. Ramazanov & M. A. Magomedov

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  1. A. K. Murtazaev
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  2. T. R. Rizvanova
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  3. M. K. Ramazanov
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  4. M. A. Magomedov
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Correspondence to A. K. Murtazaev.

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Translated by Yu. Ryzhkov

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Murtazaev, A.K., Rizvanova, T.R., Ramazanov, M.K. et al. Phase Transitions and the Thermodynamic Properties of the Potts Model with the Spin State Number q = 4 at a Kagome Lattice. Phys. Solid State 62, 1434–1438 (2020). https://doi.org/10.1134/S1063783420080247

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  • DOI: https://doi.org/10.1134/S1063783420080247

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