Numerical investigation of logarithmic corrections in two-dimensional spin models

  • B. Berche
  • L. N. Shchur
Condensed Matter

Abstract

The analysis of correlation function data obtained by Monte Carlo simulations of the two-dimensional four-state Potts model, XY model, and self-dual disordered Ising model at criticality are presented. We study the logarithmic corrections to the algebraic decay exhibited in these models. A conformal mapping is used to relate the finite-geometry information to that of the infinite plane. Extraction of the leading singularity is altered by the expected logarithmic corrections, and we show numerically that both leading and correction terms are mutually consistent.

PACS numbers

05.50.+q 75.10.Hk 

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References

  1. 1.
    M. P. M. den Nijs, J. Phys. A 12, 1857 (1979); B. Nienhuis, J. Phys. A 15, 199 (1982); Vl. S. Dotsenko and V. A. Fateev, Nucl. Phys. B 240 (12), 312 (1984).CrossRefADSGoogle Scholar
  2. 2.
    F. Y. Wu, Rev. Mod. Phys. 54, 235 (1982).CrossRefADSGoogle Scholar
  3. 3.
    N. D. Mermin and H. Wagner, Phys. Rev. Lett. 22, 1133 (1966); P. C. Hohenberg, Phys. Rev. 158, 383 (1967).ADSGoogle Scholar
  4. 4.
    V. L. Berezinskii, Zh. Éksp. Teor. Fiz. 59, 907 (1970) [Sov. Phys. JETP 32, 493 (1971)]; J. M. Kosterlitz and D. J. Thouless, J. Phys. C 6, 1181 (1973); J. M. Kosterlitz, J. Phys. C 7, 1046 (1974).Google Scholar
  5. 5.
    J. Villain, J. Phys. (Paris) 36, 581 (1975); J. M. Kosterlitz and D. J. Thouless, Prog. Low Temp. Phys. 78, 371 (1978); C. Itzykson and J. M. Drouffe, Statistical Field Theory (Cambridge Univ. Press, Cambridge, 1989), Vol. 1; J. L. Cardy, Scaling and Renormalization in Statistical Physics (Cambridge Univ. Press, Cambridge, 1996).Google Scholar
  6. 6.
    A. B. Harris, J. Phys. C 7, 1671 (1974).ADSGoogle Scholar
  7. 7.
    Vl. S. Dotsenko and Vik. S. Dotsenko, Adv. Phys. 32, 129 1983).CrossRefADSMathSciNetGoogle Scholar
  8. 8.
    R. Shankar, Phys. Rev. Lett. 58, 2466 1987); 61, 2390 (1988); A. W. W. Ludwig, Phys. Rev. Lett. 61, 2388 (1988); B. N. Shalaev, Phys. Rep. 237, 129 (1994).CrossRefADSMathSciNetGoogle Scholar
  9. 9.
    J. L. Cardy, M. Nauenberg, and D. J. Scalapino, Phys. Rev. B 22, 2560 (1980).CrossRefADSMathSciNetGoogle Scholar
  10. 10.
    D. J. Amit, Y. Y. Goldschmidt, and G. Grinstein, J. Phys. A: Math. Gen. 13, 585 (1980).CrossRefADSMathSciNetGoogle Scholar
  11. 11.
    R. Kenna and A. C. Irving, Phys. Lett. B 351, 273 (1995); A. C. Irving and R. Kenna, Phys. Rev. B 53, 11568 (1996).ADSGoogle Scholar
  12. 12.
    W. Janke, Phys. Rev. B 55, 3580 (1997).CrossRefADSGoogle Scholar
  13. 13.
    A. Patrascioiu and E. Seiler, Phys. Rev. B 54, 7177 (1996).CrossRefADSGoogle Scholar
  14. 14.
    M. Campostrini, A. Pelissetto, P. Rossi, and E. Vicari, Phys. Rev. B 54, 7301 (1996).CrossRefADSGoogle Scholar
  15. 15.
    J. Balog, J. Phys. A 34, 5237 (2001); J. Balog, M. Niedermeier, F. Niedermeyer, et al., Nucl. Phys. B 618, 315 (2001).ADSMATHMathSciNetGoogle Scholar
  16. 16.
    J. K. Kim, Phys. Lett. A 223, 621 (1996).CrossRefGoogle Scholar
  17. 17.
    J. Salas and A. D. Sokal, J. Stat. Phys. 88, 567 (1997).CrossRefMathSciNetGoogle Scholar
  18. 18.
    J. S. Wang, W. Selke, Vl. S. Dotsenko, and V. B. Andreichenko, Europhys. Lett. 11, 301 (1990).ADSGoogle Scholar
  19. 19.
    I. Rešs and J. Straley, Phys. Rev. B 61, 14425 (2000); B. Berche, Phys. Lett. A 302, 336 (2002); B. Berche, A. I. Fariñas Sanchez, and V. R. Paredes, Europhys. Lett. 60, 539 (2002); B. Berche, J. Phys. A 36, 585 (2003).Google Scholar
  20. 20.
    B. Berche and C. Chatelain, cond-mat/0207421.Google Scholar
  21. 21.
    T. W. Burkhardt and B. Derrida, Phys. Rev. B 32, 7273 (1985).CrossRefADSGoogle Scholar

Copyright information

© MAIK "Nauka/Interperiodica" 2004

Authors and Affiliations

  • B. Berche
    • 1
  • L. N. Shchur
    • 1
    • 2
  1. 1.Laboratoire de Physique des MatériauxUniversité Henri PoincaréVandoeuvre les Nancy CedexFrance
  2. 2.Landau Institute for Theoretical PhysicsRussian Academy of SciencesChernogolovka, Moscow regionRussia

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