Skip to main content
SpringerLink
Log in

Specific Features of the Effect of Structural Defects on the Correlation and Interaction of Vortex Excitations in the Nonequilibrium BKT Dynamics of the Two-Dimensional XY Model

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

Abstract

A Monte Carlo simulation of the nonequilibrium critical behavior is carried out for the two-dimensional structurally disordered XY model during its evolution from a high-temperature initial state. The features of the effect of structural disorder on the time dependence of the correlation length ξ(t) of the system and the dynamical scaling of the spin-spin autocorrelation function CSS(t, tw) are revealed. A direct calculation of the dynamic behavior of the correlation length ξ(t) of the two-dimensional structurally disordered XY model is carried out, and it is shown that this model, just as the pure model, exhibits a time dependence with a logarithmic correction ξ(t) ∝ (t/lnt)1/2, which is associated with the nonequilibrium annihilation of vortices and antivortices in the forming vortex pairs. Based on the analysis of the time dependence of the correlation length ξ(t) and the magnetization cumulant g2(t), it is shown that the two-dimensional XY model with the spin concentration p = 0.7 is so close to the spin percolation threshold pc that the influence of the attraction of the percolation fixed point becomes crucial for the relaxation properties of the system. However, the features of the critical dynamics of systems with spin concentrations of p = 0.9 and p = 0.8 are determined by the attraction of the pure fixed point. Temperature and concentration dependences of the Fisher critical exponent η(p, T) are determined using the scaling properties of the calculated two-time dependence of the spin-spin autocorrelation function CSS(t, tw). The scaling functions of the two-time dependence of the spin-spin autocorrelation function CSS(t, tw) are calculated using the dynamic dependence of the correlation length ξ(t) obtained as a result of simulation, and the values of the decay exponents λC(p, T) of the scaling functions in the long-time regime are determined, which are in good agreement with the relation λC(p, T) = 1 + η(p, T) and prove that the dynamical scaling is realized for the nonequilibrium characteristics of structurally disordered systems.

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.

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.
Fig. 10.
Fig. 11.
Fig. 12.
Fig. 13.
Fig. 14.
Fig. 15.
Fig. 16.
Fig. 17.
Fig. 18.

Similar content being viewed by others

REFERENCES

  1. V. L. Berezinskii, Sov. Phys. JETP 32, 493 (1970).

    ADS  MathSciNet  Google Scholar 

  2. V. L. Berezinskii, Low-Temperature Properties of Two-Dimensional Systems (Fizmatlit, Moscow, 2007) [in Russian].

    Google Scholar 

  3. J. M. Kosterlitz and D. J. Thouless, J. Phys. C: Solid State Phys. 6, 1181 (1973).

    Article  ADS  Google Scholar 

  4. J. M. Kosterlitz, J. Phys. C 7, 1046 (1974).

    Article  ADS  Google Scholar 

  5. L. Berthier, P. C. W. Holdsworth, and M. Sellitto, J. Phys. A 34, 1805 (2001).

    Article  ADS  MathSciNet  Google Scholar 

  6. P. V. Prudnikov, V. V. Prudnikov, and I. S. Popov, JETP Lett. 101, 539 (2015).

    Article  ADS  Google Scholar 

  7. V. V. Prudnikov, P. V. Prudnikov, and M. V. Mamonova, Phys. Usp. 60, 762 (2017).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  9. A. Taroni, S. T. Bramwell, and P. C. W. Holdsworth, J. Phys.: Condens. Matter 20, 275233 (2008).

    ADS  Google Scholar 

  10. C. A. F. Vaz, J. A. C. Bland, and G. Lauhoff, Rep. Progr. Phys. 71, 056501 (2008).

    Article  ADS  Google Scholar 

  11. C. Kawabat and A. R. Bishop, Solid State Commun. 60, 167 (1986).

    ADS  Google Scholar 

  12. H.-J. Elmers, J. Hauschild, G. H. Liu, and U. Grad mann, J. Appl. Phys. 79, 4984 (1996).

    Article  ADS  Google Scholar 

  13. J. Als-Nielsen et al., J. Phys.: Condens. Matter 5, 7871 (1993).

    ADS  Google Scholar 

  14. C. Bellitto et al., Inorg. Chem. 26, 191 (1987).

    Article  Google Scholar 

  15. A. Paduan-Filho and C. C. Becerra, J. Appl. Phys. 91, 8294 (2002).

    Article  Google Scholar 

  16. Yu. S. Karimov and Yu. N. Novikov, JETP Lett. 19, 159 (1974).

    ADS  Google Scholar 

  17. D. J. Bishop and J. D. Reppy, Phys. Rev. Lett. 40, 1727 (1978).

    Article  ADS  Google Scholar 

  18. D. J. Bishop and J. D. Reppy, Phys. Rev. B 22, 5171 (1980).

    Article  ADS  Google Scholar 

  19. S. Misra, L. Urban, M. Kim, G. Sambandamurthy, and A. Yazdani, Phys. Rev. Lett. 110, 037002 (2013).

    Article  ADS  Google Scholar 

  20. M. R. Beasley, J. E. Mooij, and T. P. Orlando, Phys. Rev. Lett. 41, 1165 (1979).

    Article  ADS  Google Scholar 

  21. A. F. Hebard and A. T. Fiory, Phys. Rev. Lett. 44, 291 (1980).

    Article  ADS  Google Scholar 

  22. L. N. Bulaevskii, V. V. Kuzii, and A. A. Sobyanin, JETP Lett. 25, 290 (1977).

    ADS  Google Scholar 

  23. A. I. Buzdin, L. N. Bulaevskii, and S. V. Panyukov, JETP Lett. 35, 178 (1982).

    ADS  Google Scholar 

  24. A. I. Buzdin, B. Vuichich, and M. Yu. Kupriyanov, Sov. Phys. JETP 74, 124 (1992).

    Google Scholar 

  25. A. N. Pargellis, S. Green, and B. Yurke, Phys. Rev. E 49, 4250 (1994).

    Article  ADS  Google Scholar 

  26. W. Bietenholz, U. Gerber, and F. G. Rejón-Barrera, J. Stat. Mech., P12009 (2013).

  27. A. Singh, S. Ahmad, S. Puri, and S. Singh, Eur. Phys. Lett. 100, 36004 (2012).

    Article  ADS  Google Scholar 

  28. A. J. Bray, Adv. Phys. 43, 357 (1994).

    Article  ADS  Google Scholar 

  29. A. J. Bray, Adv. Phys. 51, 481 (2002).

    Article  ADS  Google Scholar 

  30. W. J. Nuttall, D. Y. Noh, B. O. Wells, and R. J. Birgeneau, J. Phys.: Condens. Matter 7, 4337 (1995).

    ADS  Google Scholar 

  31. I. F. Lyuksutov and A. G. Fedorus, Sov. Phys. JETP 53, 1317 (1981).

    Google Scholar 

  32. P. Tabeling, Phys. Rep. 362, 1 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  33. S. Abriet and D. Karevski, Eur. Phys. J. B 37, 47 (2004).

    Article  ADS  Google Scholar 

  34. X. W. Lei and B. Zheng, Phys. Rev. E 75, 040104(R) (2007).

  35. V. V. Prudnikov, P. V. Prudnikov, S. V. Alekseev, and I. S. Popov, Phys. Met. Metalogr. 115, 1186 (2014).

    Article  Google Scholar 

  36. V. V. Prudnikov, P. V. Prudnikov, and I. S. Popov, J. Exp. Theor. Phys. 126, 368 (2018).

    Article  ADS  Google Scholar 

  37. P. V. Prudnikov and I. S. Popov, J. Phys.: Conf. Ser. 510, 012014 (2014).

    Google Scholar 

  38. M. V. Mamonova, I. S. Popov, P. V. Prudnikov, V. V. Prudnikov, and A. N. Purtov, Lobachevskii J. Math. 38, 944 (2017).

    Article  MathSciNet  Google Scholar 

  39. F. Krzakala and F. Ricci-Tersenghi, J. Phys.: Conf. Ser. 40, 42 (2006).

    ADS  MathSciNet  Google Scholar 

  40. I. S. Popov and P. V. Prudnikov, Solid State Phenom. 233–234, 8 (2015).

  41. I. S. Popov, P. V. Prudnikov, and V. V. Prudnikov, J. Phys.: Conf. Ser. 681, 012015 (2016).

    Google Scholar 

  42. P. V. Prudnikov, V. V. Prudnikov, E. A. Pospelov, et al., Prog. Theor. Exp. Phys. 2015, 053A01 (2015).

  43. V. V. Prudnikov, P. V. Prudnikov, and E. A. Pospelov, J. Stat. Mech., 043303 (2016).

  44. A. R. Pereira, L. A. S. Mól, S. A. Leonel, P. Z. Coura, and B. V. Costa, Phys. Rev. B 68, 132409 (2003).

    Article  ADS  Google Scholar 

  45. B. Berche, A. I. Farinas-Sanchez, Yu. Holovatch, and R. Paredes, Eur. Phys. J. B 36, 91 (2003).

    Article  ADS  Google Scholar 

  46. O. Kapikranian, B. Berche, and Yu. Holovatch, Eur. Phys. J. B 56, 93 (2007).

    Article  ADS  Google Scholar 

  47. A. D. Rutenberg and A. J. Bray, Phys. Rev. E 51, 5499 (1995).

    Article  ADS  Google Scholar 

  48. A. J. Bray, A. J. Briant, and D. K. Jervis, Phys. Rev. Lett. 84, 1503 (2000).

    Article  ADS  Google Scholar 

  49. F. Rojas and A. D. Rutenberg, Phys. Rev. E 60, 212 (1999).

    Article  ADS  Google Scholar 

  50. A. Jelić and L. F. Cugliandolo, J. Stat. Mech., P02032 (2011).

  51. A. Asad and B. Zheng, J. Phys. A 40, 9957 (2007).

    Article  ADS  MathSciNet  Google Scholar 

  52. R. Loft and T. A. Deorand, Phys. Rev. B 35, 8528 (1987).

    Article  ADS  Google Scholar 

  53. B. Yurke, A. N. Pargellis, T. Kovacs, and D. A. Huse, Phys. Rev. E 47, 1525 (1993).

    Article  ADS  Google Scholar 

  54. A. J. Bray and A. D. Rutenberg, Phys. Rev. E 49, R27 (1994).

    Article  ADS  Google Scholar 

  55. C. Godreche and J. M. Luck, J. Phys. A 33, 1151 (2000);

    Article  ADS  MathSciNet  Google Scholar 

  56. J. Phys. A 33, 9141 (2000).

  57. M. Henkel, Nucl. Phys. B 641, 405 (2002).

    Article  ADS  Google Scholar 

  58. M. Henkel, M. Paessens, and M. Pleimling, Europhys. Lett. 62, 664 (2003).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  60. A. R. Pereira, J. Magn. Magn. Mater. 279, 396 (2004).

    Article  ADS  Google Scholar 

  61. H. Weber and P. Minnhagen, Phys. Rev. B 37, 5986 (1988).

    Article  ADS  Google Scholar 

  62. I. S. Popov, A. P. Popova, P. V. Prudnikov, and V. V. Prudnikov, J. Phys.: Conf. Ser. 1163, 012042 (2019).

    Google Scholar 

  63. I. S. Popov, A. P. Popova, and P. V. Prudnikov, J. Phys.: Conf. Ser. 1163, 012039 (2019).

    Google Scholar 

  64. I. S. Popov, A. P. Popova, and P. V. Prudnikov, J. Phys.: Conf. Ser. 1389, 012024 (2019).

    Google Scholar 

  65. I. S. Popov, A. P. Popova, and P. V. Prudnikov, Europhys. Lett. 128, 26002 (2019).

    Article  ADS  Google Scholar 

  66. R. M. Ziff and B. Sapoval, J. Phys. A: Math. Gen. 19, L1169 (1986).

    Article  ADS  Google Scholar 

  67. A. A. Sorokin, S. V. Makogonov, and S. P. Korolev, Nauch.-Tekh. Inform., Ser. 1: Organiz. Metod. Inform. Raboty 12, 14 (2017).

    Google Scholar 

Download references

Funding

This work was supported by the Russian Foundation for Basic Research (projects nos. 17-02-00279, 18-32-00814, 18-42-550003, and 20-32-70189), by the Ministry of Science and Higher Education of the Russian Federation within the state assignment (project no. 0741-2020-0002), and by grants MD-4349.2018.2 and MD-2229.2020.2 of the President of the Russian Federation. The computations were performed on the facilities of the Data Center of the Far Eastern Branch of the Russian Academy of Sciences [66], the Joint Supercomputer Center of the Russian Academy of Sciences, and the Moscow State University Supercomputer Center.

Author information

Authors and Affiliations

  1. Omsk State University, 644077, Omsk, Russia

    V. V. Prudnikov, P. V. Prudnikov & I. S. Popov

Authors
  1. V. V. Prudnikov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. V. Prudnikov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. I. S. Popov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. V. Prudnikov.

Additional information

Translated by I. Nikitin

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Prudnikov, V.V., Prudnikov, P.V. & Popov, I.S. Specific Features of the Effect of Structural Defects on the Correlation and Interaction of Vortex Excitations in the Nonequilibrium BKT Dynamics of the Two-Dimensional XY Model. J. Exp. Theor. Phys. 131, 768–792 (2020). https://doi.org/10.1134/S1063776120110096

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063776120110096

Search

Navigation