Skip to main content
Log in

Phase Transitions in the Clock Model with q = 5 Spin States on a Triangular Lattice

  • ORDER, DISORDER, AND PHASE TRANSITION IN CONDENSED SYSTEM
  • Published:
Journal of Experimental and Theoretical Physics Aims and scope Submit manuscript

Abstract

The phase transitions and thermodynamic properties of the clock model with q = 5 spin states on a triangular lattice have been investigated using the Wang–Landau Monte Carlo algorithm. The phase transitions have been analyzed with the histogram method and the fourth-order Binder cumulant method. Two Berezinskii–Kosterlitz–Thouless phase transitions are shown to be observed in the ferromagnetic clock model, while a second-order phase transition has been detected in the antiferromagnetic clock model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.

REFERENCES

  1. L. E. Svistov, L. A. Prozorova, N. Byuttgen, A. Ya. Shapiro, and L. N. Dem’yanets, JETP Lett. 81, 102 (2005).

    Article  ADS  Google Scholar 

  2. S. E. Korshunov, Phys. Usp. 49, 225 (2006).

    Article  ADS  Google Scholar 

  3. M. Tisser, B. Delamotte, and D. Mouhanna, Phys. Rev. Lett. 84, 5208 (2000).

    Article  ADS  Google Scholar 

  4. P. Calabrese, P. Parruccini, A. Pelissetto, et al., Phys. Rev. B 70, 174439 (2004).

  5. M. K. Badiev, A. K. Murtazaev, M. K. Ramazanov, and M. A. Magomedov, J. Exp. Theor. Phys. 134, 644 (2022).

    Article  ADS  Google Scholar 

  6. A. I. Smirnov, H. Yashiro, S. Kimura, et al., Phys. Rev. B 75, 134412 (2007).

  7. J. L. Jacobsen, J. Salas, and C. R. Scullard, J. Phys. A: Math. Theor. 50, 345002 (2017).

  8. E. Z. Ising, Phys. 31, 253 (1924).

    Google Scholar 

  9. G. H. Wannier, Phys. Rev. 79, 357 (1950).

    Article  ADS  MathSciNet  Google Scholar 

  10. M. Tisser, B. Delamotte, and D. Mouhanna, Phys. Rev. Lett. 84, 5208 (2000).

    Article  ADS  Google Scholar 

  11. A. K. Murtazaev, M. K. Badiev, M. K. Ramazanov, et al., Phase Trans. 94, 394 (2021).

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  13. Rev. Mod. Phys. 55, 315(E) (1983).

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

    Article  ADS  Google Scholar 

  15. C. Itzykson, H. Saleur, and J.-B. Zuber, Conformal Invariance and Applications to Statistical Mechanics (World Scientific, Singapore, 1988).

    Google Scholar 

  16. E. Rastellia, S. Reginaa, and A. Tassi, J. Magn. Magn. Mater. 272, 997 (2004).

    Article  ADS  Google Scholar 

  17. S. S. Murty, Challa, and D. P. Landau, Phys. Rev. B 33, 437 (1986).

    Google Scholar 

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

    Article  ADS  Google Scholar 

  19. Li Guanrong, H. P. Kwok, and G. Zheng-Cheng, arXiv: 2009.10695v1 [cond-mat.stat-mech] (2020).

  20. Li Zi-Qian, Li-Ping Yang, Z. Y. Xie, et al., Phys. Rev. E 101, 060105(R) (2020).

  21. G. Ortiz, E. Cobanera, and Z. Nussinov, Nucl. Phys. B 854, 780 (2012).

    Article  ADS  Google Scholar 

  22. Y. Kumano, K. Hukushima, Y. Tomita, et al., Phys. Rev. B 88, 104427 (2013).

  23. O. A. Negrete, P. Vargas, F. J. Pena, et al., Entropy 20, 933 (2018).

    Article  ADS  Google Scholar 

  24. S. Chatterjee, S. Puri, and R. Paul, Phys. Rev. E 98, 032109 (2018).

  25. T. Surungan, S. Masuda, Y. Komura, et al., J. Phys. A 52, 275002 (2019).

  26. C. O. Hwang, Phys. Rev. E 80, 042103 (2009).

  27. N. D. Mermin and H. Wagner, Phys. Rev. Lett. 17, 1133 (1966).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  29. M. K. Ramazanov, A. K. Murtazaev, and M. A. Magomedov, J. Exp. Theor. Phys. 134, 693 (2022).

    Article  ADS  Google Scholar 

  30. M. K. Ramazanov and A. K. Murtazaev, JETP Lett. 109, 589 (2019).

    Article  ADS  Google Scholar 

  31. M. K. Ramazanov, A. K. Murtazaev, M. A. Magomedov, and M. K. Mazagaeva, JETP Lett. 114, 693 (2021).

    Article  ADS  Google Scholar 

  32. A. K. Murtazaev, M. K. Badiev, M. K. Ramazanov, et al., Phys. A (Amsterdam, Neth.) 555, 124530 (2020).

  33. R. Masrour, A. Jabar, A. Benyoussef, et al., J. Magn. Magn. Mater. 401, 695 (2016).

    Article  ADS  Google Scholar 

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

  35. Y. Chen, Z. Y. Xie, and J. F. Yu, Chin. Phys. B 27, 080503 (2018).

  36. K. Eichhorn and K. Binder, J. Phys.: Condens. Matter 8, 5209 (1996).

    ADS  Google Scholar 

  37. D. Loison and K. D. Schotte, Eur. Phys. J. B 5, 735 (1998).

    Article  ADS  Google Scholar 

Download references

Funding

This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. K. Badiev.

Ethics declarations

The authors of this work declare that they have no conflicts of interest.

Additional information

Translated by V. Astakhov

Publisher’s Note.

Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Murtazaev, A.K., Badiev, M.K., Magomedov, M.A. et al. Phase Transitions in the Clock Model with q = 5 Spin States on a Triangular Lattice. J. Exp. Theor. Phys. 137, 682–687 (2023). https://doi.org/10.1134/S1063776123110080

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063776123110080

Navigation