Skip to main content
SpringerLink
Log in

Phase Transitions and Critical Phenomena in the 2D Potts Impurity Model on a Square Lattice

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

Abstract

Phase transitions and critical behavior in the 2D dilute Potts model with number q = 4 of spin states on a square lattice are investigated by computer simulation. Systems with linear sizes L × L = N, l = 10–160 with spin concentrations p = 1.00, 0.95, 0.80 are considered. It is shown that the introduction of magnetic impurities plays a stabilizing role in the realization of a second-order phase transition in the Potts model under investigation. Based on the finite-size scaling theory, statistical critical indices of heat capacity α, susceptibility γ, magnetization β, and correlation radius index ν are calculated for the range of concentrations p considered here.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.

Similar content being viewed by others

REFERENCES

  1. L. N. Shchur, Phys. Usp. 55, 733 (2012).

    Article  Google Scholar 

  2. O. Vasilyev, B. Berche, M. Dudka and Yu. Holovatch, Phys. Rev. E 92, 042118 (2015).

  3. D. P. Landau and K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics (Cambridge Univ. Press, Cambridge, 2014).

    Book  Google Scholar 

  4. R. Fol’k, Yu. Golovach, and T. Yavorskii, Phys. Usp. 46, 169 (2003).

    Article  ADS  Google Scholar 

  5. V. S. Dotsenko, Phys. Usp. 46, 169 (2003).

    Article  Google Scholar 

  6. A. B. Harris, J. Phys. C 7, 1671 (1974).

    Article  ADS  Google Scholar 

  7. A. N. Vakilov and V. V. Prudnikov, JETP Lett. 55, 741 (1992).

    ADS  Google Scholar 

  8. A. B. Babaev and A. K. Murtazaev, Math. Models Comput. Simul. 11, 575 (2019).

    Article  MathSciNet  Google Scholar 

  9. Vik. Dotsenko and Vl. Dotsenko, Adv. Phys. 32, 129 (1983).

  10. M. Aizenman and J. Wehr, Phys. Rev. Lett. 62, 2503 (1989).

    Article  ADS  MathSciNet  Google Scholar 

  11. V. V. Dubs, V. V. Prudnikov, and P. V. Prudnikov, Theor. Math. Phys. 190, 359 (2017).

    Article  Google Scholar 

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

    MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  14. L. Schwenger, K. Budde, C. Voges, and H. Pfnur, Phys. Rev. Lett. 73, 296 (1994).

    Article  ADS  Google Scholar 

  15. A. B. Babaev and A. K. Murtazaev, Phys. Solid State 62, 851 (2020).

    Article  ADS  Google Scholar 

  16. A. B. Babaev and A. K. Murtazaev, J. Phys.: Conf. Ser. 1389, 1 (2019).

    Google Scholar 

  17. U. Wolff, Phys. Lett. 62, 361 (1989).

    Article  Google Scholar 

  18. A. B. Babaev and A. K. Murtazaev, Vestn. Omsk. Univ. 25, 7 (2020).

    Google Scholar 

  19. G. T. Barkema and M. E. J. Newman, cond-mat/9703179.

  20. P. Peczac, A. M. Ferrenberg, and D. P. Landau, Phys. Rev. B 43, 6087 (1991).

    Article  ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  23. A. K. Murtazaev and A. B. Babaev, Mater. Lett. 258, 126771 (2020).

  24. A. K. Murtazaev, A. B. Babaev, and G. Y. Ataeva, J. Magn. Magn. Mater. 440, 101 (2017).

    Article  ADS  Google Scholar 

  25. A. K. Murtazaev and A. B. Babaev, JETP Lett. 99, 535 (2014).

    Article  ADS  Google Scholar 

  26. M. E. Fisher and M. N. Barber, Phys. Rev. Lett. 28, 1516 (1972).

    Article  ADS  Google Scholar 

  27. D. Loison, Phys. Lett. 257, 83 (1999).

    Article  Google Scholar 

  28. B. N. Shalaev, Phys. Rep. 237, 129 (1994).

    Article  ADS  MathSciNet  Google Scholar 

  29. J. L. Cardy, M. Nauenberg, and D. J. Scalpino, Phys. Rev. 22, 2560 (1980).

    Article  ADS  MathSciNet  Google Scholar 

  30. J. S. Salas and A. D. Sokal, J. Stat. Phys. 88, 567 (1996).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Amirkhanov Institute of Physics, Dagestan Federal Research Center, Russian Academy of Sciences, 367003, Makhachkala, Russia

    A. K. Murtazaev, A. B. Babaev, G. Ya. Ataeva & M. A. Magomedov

  2. Dagestan Federal Research Center, Russian Academy of Sciences, 367000, Makhachkala, Russia

    A. B. Babaev & M. A. Magomedov

Authors
  1. A. K. Murtazaev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. B. Babaev
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. Ya. Ataeva
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. A. Magomedov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. B. Babaev.

Ethics declarations

The authors declare that they have no conflicts of interest.

Additional information

Translated by N. Wadhwa

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Murtazaev, A.K., Babaev, A.B., Ataeva, G.Y. et al. Phase Transitions and Critical Phenomena in the 2D Potts Impurity Model on a Square Lattice. J. Exp. Theor. Phys. 135, 347–353 (2022). https://doi.org/10.1134/S1063776122090072

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063776122090072

Search

Navigation