Skip to main content
Log in

Abstract

We study the non-equilibrium time evolution of the classical XY spin model in two dimensions. The two-time autocorrelation and linear response functions are considered for systems initially prepared in a high temperature state and in a completely ordered state. After a quench into the critical phase, we use Monte Carlo simulations to determine the time-evolution of these quantities, and we deduce the temperature dependence of the slope of the parametric plot susceptibility/correlation in the asymptotic regime. This slope is usually identified with the infinite fluctuation-dissipation ratio, which measures the extent of violation of the equilibrium fluctuation-dissipation theorem. However, a direct measure of this ratio leads to a vanishing value.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. J.-P. Bouchaud, L.F. Cugliandolo, J. Kurchan, M. Mézard, in Spin Glasses and Random Fields, edited by A.P. Young (World Scientific, Singapore, 1998)

  2. A. Crisanti, F. Ritort, J. Phys. A 36, R181 (2003)

  3. L.F. Cugliandolo, J. Kurchan, Phys. Rev. Lett. 71, 173 (1993); J. Phys. A 27, 5749 (1994)

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  5. M. Henkel, M. Pleiming, C. Godreche, J.-M. Luck, Phys. Rev. Lett. 87, 265701 (2001); for a recent review see M. Henkel, A. Picone, M. Pleimling, J. Unterberger, cond-mat/0307649

    Article  ADS  Google Scholar 

  6. L.F. Cugliandolo, J. Kurchan, G. Parisi, J. Phys. I France 14, 1641 (1994)

    Article  Google Scholar 

  7. C. Godréche, J.-M. Luck, J. Phys. A 33, 1151 (2000); C. Godréche, J.-M. Luck, J. Phys. A 33, 9141 (2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. For a recent review see C. Godréche, J.-M. Luck, J. Phys. Condens. Matter 14, 1589 (2002)

    Article  ADS  Google Scholar 

  9. P. Calabrese, A. Gambassi, Phys. Rev. E 65, 066120 (2002); P. Calabrese, A. Gambassi, Phys. Rev. E 66, 212407 (2002)

    Article  ADS  Google Scholar 

  10. F. Sastre, I. Dornic, H. Chaté, cond-mat/0308178

  11. M. Henkel, G.M. Schütz, J. Phys. A 37, 591 (2004); P. Mayer, P. Sollich, J. Phys. A 37, 9 (2004)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. L.F. Cugliandolo, Lecture Notes, Les Houches, July 2002, Session LXXVII (EDP Sciences, Springer-Verlag, 2003)

  13. E. Lippiello, M. Zannetti, Phys. Rev. E 61, 3369 (2000)

    Article  ADS  Google Scholar 

  14. L.F. Cugliandolo, J. Kurchan, L. Peliti, Phys. Rev. E 55, 3898 (1997)

    Article  ADS  Google Scholar 

  15. C. Chatelain, J. Phys. A 36, 10739 (2003); F. Ricci-Tersenghi, Phys. Rev. E 68, R065104 (2003)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. V.L. Berezinskii, Sov. Phys. JETP 32, 493 (1971)

    MathSciNet  ADS  Google Scholar 

  17. J.M. Kosterlitz, D.J. Thouless, J. Phys. C 6, 1181 (1973); J.M. Kosterlitz, J. Phys. C 7, 1046 (1974); J. Villain, J. Phys. France 36, 581 (1975)

    Article  ADS  Google Scholar 

  18. B. Berche, J. Phys. A 36, 585 (2003)

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  22. A. Barrat, Phys. Rev. E 57, 3629 (1998)

    Article  ADS  Google Scholar 

  23. We take the same value as in reference [20] in order to have a direct comparison of our results with those of Berthier et al..

  24. A. Picone, M. Henkel, J. Phys. A 35, 5575 (2002)

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to D. Karevski.

Additional information

Received: 15 September 2003, Published online: 19 February 2004

PACS:

75.40.Gb Dynamic properties - 05.70.Ln Non-equilibrium and irreversible thermodynamics

Rights and permissions

Reprints and permissions

About this article

Cite this article

Abriet, S., Karevski, D. Off equilibrium dynamics in the 2d-XY system. Eur. Phys. J. B 37, 47–53 (2004). https://doi.org/10.1140/epjb/e2004-00029-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjb/e2004-00029-9

Keywords

Navigation