Skip to main content
SpringerLink
Log in

Critical thermodynamics of two-dimensional systems in the five-loop renormalization-group approximation

  • Low-Dimensional Systems and Surface Physics
  • Published:
Physics of the Solid State Aims and scope Submit manuscript

Abstract

The paper is devoted to the calculation of renormalization-group (RG) functions in the O(n)-symmetry two-dimensional model of the λϕ 4 type in the five-loop approximation and to an analysis of the critical behavior of systems described by this model. Five-loop expansions for the β function and the critical indices are determined in bulk theory. They are summed up using the Padé-Borel and Padé-Borel-Le Roy methods, making it possible to optimize the summation procedure and to estimate the accuracy of the obtained numerical values. It is shown that in the Ising (n=1) case, as well as in other cases, the inclusion of the five-loop contribution to the β function displaces the coordinate of the Wilson fixed point only insignificantly, leaving it outside the interval formed by the results of computations on lattices; even “spreads” of the error in the renormalization group and lattice estimates do not overlap. This discrepancy is attributed to the effect of the nonanalytic com-ponent of the β function, which cannot be determined in perturbation theory. A computation of critical indices proves that, although the inclusion of the five-loop terms in the corresponding RG expansion slightly improves the concordance with the exact results, the nonanalytic contributions are apparently also significant in this case.

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

Similar content being viewed by others

References

  1. G. A. Baker, B. G. Nickel, and D. I. Meiron, Phys. Rev. B 17(3), 1365 (1978).

    Article  ADS  Google Scholar 

  2. J. C. Le Guillou and J. Zinn-Justin, Phys. Rev. B 21(9), 3976 (1980).

    ADS  MathSciNet  Google Scholar 

  3. S. A. Antonenko and A. I. Sokolov, Phys. Rev. E 51(3), 1894 (1995).

    Article  ADS  Google Scholar 

  4. R. Guida and J. Zinn-Justin, Nucl. Phys. B 489(3), 626 (1997).

    Article  ADS  Google Scholar 

  5. H. Kleinert, Phys. Rev. D 57(4), 2264 (1998).

    Article  ADS  Google Scholar 

  6. A. I. Sokolov, Fiz. Tverd. Tela (S.-Peterburg) 40(7), 1284 (1998) [Phys. Solid State 40, 1169 (1998)].

    Google Scholar 

  7. R. Guida and J. Zinn-Justin, J. Phys. A 31(40), 8103 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  8. H. Kleinert, Phys. Rev. D 60, 085001 (1999).

    Google Scholar 

  9. A. I. Sokolov, E. V. Orlov, V. A. Ul’kov, and S. S. Kashtanov, Phys. Rev. E 60(2), 1344 (1999).

    Article  ADS  Google Scholar 

  10. B. Nienhuis, Phys. Rev. Lett. 49(15), 1062 (1982).

    Article  ADS  MathSciNet  Google Scholar 

  11. B. Nienhuis, J. Stat. Phys. 34, 731 (1984).

    Article  MATH  MathSciNet  Google Scholar 

  12. D. Friedan, Z. Qiu, and S. Shenker, Phys. Rev. Lett. 52(18), 1575 (1984).

    Article  ADS  MathSciNet  Google Scholar 

  13. J. Salas and A. Sokal, J. Stat. Phys. 98(3/4) (2000) (in press); Preprint no. cond-mat/9904038 (1999).

  14. M. Caselle, M. Hasenbusch, A. Pelissetto, and E. Vicari, Preprint no. hep-th/0003049 (2000).

  15. A. I. Sokolov and E. V. Orlov, Phys. Rev. B 58(5), 2395 (1998).

    Article  ADS  Google Scholar 

  16. S. Y. Zinn, S. N. Lai, and M. E. Fisher, Phys. Rev. E 54(2), 1176 (1996).

    Article  ADS  Google Scholar 

  17. A. Pelissetto and E. Vicari, Nucl. Phys. B 522(3), 605 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  18. B. G. Nickel, D. I. Meiron, and G. A. Baker, Jr., Compilation of 2-pt and 4-pt Graphs for Continuous Spin Model, University of Guelph Report (1977).

  19. G. A. Baker, Jr. and P. Graves-Morris, Pade Approximants (Addison-Wesley, Reading, 1981; Mir, Moscow, 1986).

    Google Scholar 

  20. I. O. Mayer, J. Phys. A 22(14), 2815 (1989).

    Article  ADS  Google Scholar 

  21. G. A. Baker, Jr., Phys. Rev. B 15, 1552 (1977).

    Article  ADS  Google Scholar 

  22. P. Butera and M. Comi, Phys. Rev. B 54(22), 15828 (1996).

  23. A. Pelissetto and E. Vicari, Nucl. Phys. B 519(3), 626 (1998).

    Article  ADS  Google Scholar 

  24. M. Campostrini, A. Pelissetto, P. Rossi, and E. Vicari, Nucl. Phys. B 459(1), 207 (1996).

    Article  ADS  Google Scholar 

  25. J. K. Kim and A. Patrascioiu, Phys. Rev. D 47, 2588 (1993).

    ADS  Google Scholar 

  26. G. Jug and B. N. Shalaev, J. Phys. A 32(42), 7249 (1999).

    Article  ADS  MathSciNet  Google Scholar 

  27. J. Zinn-Justin, Quantum Field Theory and Critical Phenomena (Clarendon, Oxford, 1996).

    Google Scholar 

  28. B. G. Nickel, Physica A (Amsterdam) 117, 189 (1981).

    Google Scholar 

  29. J. Kim, Phys. Lett. B 345, 469 (1995).

    ADS  Google Scholar 

  30. J. C. Le Guillou and J. Zinn-Justin, J. Phys. Lett. (Paris) 46, L137 (1985); J. Phys. (Paris) 48, 19 (1987); 50, 1365 (1989).

    Google Scholar 

  31. B. Nienhus, J. Phys. A 15, 199 (1982).

    ADS  MathSciNet  Google Scholar 

  32. M. Barma and M. E. Fisher, Phys. Rev. Lett. 53(20), 1935 (1984).

    Article  ADS  Google Scholar 

  33. E. Barouch, B. M. McCoy, and T. T. Wu, Phys. Rev. Lett. 31(23), 1409 (1973).

    Article  ADS  Google Scholar 

  34. M. Henkel, Conformal Invariance and Critical Phenomena (Springer, New York, 1999).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. St. Petersburg State University of Electrical Engineering, St. Petersburg, 197376, Russia

    E. V. Orlov & A. I. Sokolov

Authors
  1. E. V. Orlov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. I. Sokolov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Fizika Tverdogo Tela, Vol. 42, No. 11, 2000, pp. 2087–2093.

Original Russian Text Copyright © 2000 by Orlov, Sokolov.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Orlov, E.V., Sokolov, A.I. Critical thermodynamics of two-dimensional systems in the five-loop renormalization-group approximation. Phys. Solid State 42, 2151–2158 (2000). https://doi.org/10.1134/1.1324056

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/1.1324056

Keywords

Search

Navigation