Influence of quenched dilution on the quasi-long-range ordered phase of the \(\mathsf{2d}\) \(\mathsf{XY}\) model

  • B. Berche
  • A. I. Fariñas-Sánchez
  • Yu. Holovatch
  • R. ParedesV.


The influence of non magnetic impurities in the 2d XY model is investigated through Monte Carlo (MC) simulations. The general picture of the transition is fully understood from the Harris criterion which predicts that the universality class is unchanged, and the Berezinskii-Kosterlitz-Thouless description of the topological transition remains valid. We nevertheless address here the question about the influence of dilution on the quasi-long-range order at low temperatures. In particular, we study the asymptotic of the pair correlation function and report the MC estimates for the critical exponent \(\eta\) at different dilutions. In the weak dilution region, our MC calculations are further supported by simple spin-wave-like calculations.


Correlation Function Monte Carlo Pair Correlation General Picture Monte Carlo Calculation 
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  1. 1.
    A.B. Harris, J. Phys. C 7, 1671 (1974)CrossRefGoogle Scholar
  2. 2.
    V.L. Berezinskii, Sov. Phys. JETP 32, 493 (1971)Google Scholar
  3. 3.
    J.M. Kosterlitz, D.J. Thouless, J. Phys. C 6, 1181 (1973)CrossRefGoogle Scholar
  4. 4.
    J.M. Kosterlitz, J. Phys. C 7, 1046 (1974)CrossRefGoogle Scholar
  5. 5.
    N.D. Mermin, H. Wagner, Phys. Rev. Lett. 22, 1133 (1966)CrossRefGoogle Scholar
  6. 6.
    P.C. Hohenberg, Phys. Rev. 158, 383 (1967)CrossRefGoogle Scholar
  7. 7.
    F. Wegner, Z. Phys. 206, 465 (1967)Google Scholar
  8. 8.
    J.M. Kosterlitz, D.J. Thouless, Prog. Low Temp. Phys. 78, 371 (1978)Google Scholar
  9. 9.
    D.R. Nelson, in Phase Transitions and Critical Phenomena, edited by C. Domb, J.L. Lebowitz, (Academic Press, London 1983), p. 1Google Scholar
  10. 10.
    C. Itzykson, J.M. Drouffe, Statistical field theory, (Cambridge University Press, Cambridge 1989), Vol. 1Google Scholar
  11. 11.
    Z. Gulácsi, M. Gulácsi, Adv. Phys. 47, 1 (1998)CrossRefGoogle Scholar
  12. 12.
    P.M. Chaikin, T.C. Lubensky, Principles of Condensed Matter Physics (Cambridge University Press, Cambridge 1995)Google Scholar
  13. 13.
    M. Hasenbuch, K. Pinn, J. Phys. A 30, 63 (1997)Google Scholar
  14. 14.
    L.A.S. Mól, A.R. Pereira, A.S.T. Pires, Phys. Rev. B 66, 052415 (2002), arXiv e-print cond-mat/0208523CrossRefGoogle Scholar
  15. 15.
    S.A. Leonel, P. Zimmermann Coura, A.R. Pereira, L.A.S. Mól, B.V. Costa, Phys. Rev. B 67, 104426 (2003), arXiv e-print cond-mat/0210210CrossRefGoogle Scholar
  16. 16.
    I. Reš, J. Straley, Phys. Rev. B 61, 14425 (2000)CrossRefGoogle Scholar
  17. 17.
    B. Berche, A.I. Fariñas-Sánchez, R. Paredes V., Europhys. Lett. 60, 539, (2002) arXiv e-print cond-mat/0208521Google Scholar
  18. 18.
    B. Berche, J. Phys. A 36, 585 (2003), arXiv e-print cond-mat/0211584CrossRefGoogle Scholar
  19. 19.
    Handbook of mathematical functions, edited by M. Abramowitz, I. Stegun (National Bureau of Standards, 1964)Google Scholar
  20. 20.
    U. Wolff Nucl. Phys. B 322, 759 (1989)Google Scholar
  21. 21.
    K. Kato, S. Todo, K. Harada, N. Kawashima, S. Miyashita, H. Takayama, Phys. Rev. Lett. 84, 4204 (2000), arXiv e-print cond-mat/9905379CrossRefGoogle Scholar
  22. 22.
    A.W. Sandvik, Phys. Rev. B 66, 024418, (2002) arXiv e-print cond-mat/0110510CrossRefGoogle Scholar
  23. 23.
    R. Brout, Phys. Rev. 115, 824 (1959)CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin/Heidelberg 2003

Authors and Affiliations

  • B. Berche
    • 1
  • A. I. Fariñas-Sánchez
    • 1
    • 2
  • Yu. Holovatch
    • 3
    • 4
  • R. ParedesV.
    • 2
  1. 1.Laboratoire de Physique des MatériauxUniversité Henri Poincaré, Nancy 1 Vandœuvre les Nancy CedexFrance
  2. 2.Centro de FísicaInstituto Venezolano de Investigaciones CientíficasCaracasVenezuela
  3. 3.Institute for Condensed Matter PhysicsNational Academy of Sciences of UkraineLvivUkraine
  4. 4.Ivan Franko National University of LvivLvivUkraine

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