- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Correction to scaling in the response function of the two-dimensional kinetic Ising model

Federico Corberi*, Eugenio Lippiello†, and Marco Zannetti‡

  • Istituto Nazionale di Fisica della Materia, Unità di Salerno and Dipartimento di Fisica “E. Caianiello,” Università di Salerno, 84081 Baronissi (Salerno), Italy

  • *Electronic address: corberi@sa.infn.it
  • †Electronic address: lippiello@sa.infn.it
  • ‡Electronic address: zannetti@na.infn.it
PDF

Phys. Rev. E 72, 056103 – Published 3 November, 2005

DOI: https://doi.org/10.1103/PhysRevE.72.056103

Abstract

The aging part Rag(t,s) of the impulsive response function of the two-dimensional ferromagnetic Ising model, quenched below the critical point, is studied numerically employing an algorithm without the imposition of the external field. We find that the simple scaling form Rag(t,s)=s−(1+a)f(t∕s), which is usually believed to hold in the aging regime, is not obeyed. We analyze the data assuming the existence of a correction to scaling. We find a=0.273±0.006, in agreement with previous numerical results obtained from the zero field cooled magnetization. We investigate in detail also the scaling function f(t∕s) and we compare the results with the predictions of analytical theories. We make an ansatz for the correction to scaling, deriving an analytical expression for Rag(t,s). This gives a satisfactory qualitative agreement with the numerical data for Rag(t,s) and for the integrated response functions. With the analytical model we explore the overall behavior, extrapolating beyond the time regime accessible with the simulations. We explain why the data for the zero field cooled susceptibility are not too sensitive to the existence of the correction to scaling in Rag(t,s), making this quantity the most convenient for the study of the asymptotic scaling properties.

View figure in article

Article Text

References (33)

  1. L. F. Cugliandolo, in Trends in Theoretical Physics II, edited by H. Falomir, R. E. Gamboa Saraví, and F. A. Schaposnik, AIP Conf. Proc. No. 484 (AIP, Woodbury, NY, 1999); G. Parisi, F. Ricci-Terzenghi, and J. J. Ruiz-Lorenzo, Eur. Phys. J. B 11, 317 (1999).
  2. S. Franz, M. Mézard, G. Parisi, and L. Peliti, Phys. Rev. Lett. 81, 1758 (1998); J. Stat. Phys. 97, 459 (1999).
  3. S. Franz and M. A. Virasoro, J. Phys. A 33, 891 (2000).
  4. F. Corberi, E. Lippiello, and M. Zannetti, Phys. Rev. E 65, 046136 (2002).
  5. J. P. Bouchaud, L. F. Cugliandolo, J. Kurchan, and M. Mézard in Spin Glasses and Random Fields, edited by A. P. Young (World Scientific, Singapore, 1997).
  6. L. F. Cugliandolo, in Slow Relaxations and Nonequilibrium Dynamics in Condensed Matter, edited by J.-L. Barrat, M. V. Feigelman, J. Kurchan, and J. Dalibard, Les Houches Proceedings of the Summer School of Theoretical Physics LXXVII (Springer-Verlag, Berlin, 2004).
  7. For a review see A. J. Bray, Adv. Phys. 43, 357 (1994).
  8. F. Corberi, E. Lippiello, and M. Zannetti, J. Stat. Mech.: Theory Exp. (2004) P12007.
  9. D. S. Fisher and D. A. Huse, Phys. Rev. B 38, 373 (1988).
  10. This is no longer correct in the case of a conserved order parameter. C. Yeung, M. Rao, and R. C. Desai, Phys. Rev. E 53, 3073 (1996); C. Godreche, F. Krzakala, and F. Ricci-Tersenghi, J. Stat. Mech.: Theory Exp. (2004) P04007; C. Sire, Phys. Rev. Lett. 93, 130602 (2004); P. Calabrese and A. Gambassi, J. Phys. A 38, R133 (2005).
  11. E. Lippiello and M. Zannetti, Phys. Rev. E 61, 3369 (2000).
  12. C. Godrèche and J. M. Luck, J. Phys. A 33, 1151 (2000).
  13. F. Corberi, E. Lippiello, and M. Zannetti, Eur. Phys. J. B 24, 359 (2001).
  14. L. Berthier, J. L. Barrat, and J. Kurchan, Eur. Phys. J. B 11, 635 (1999).
  15. G. F. Mazenko, Phys. Rev. E 69, 016114 (2004).
  16. F. Corberi, E. Lippiello, and M. Zannetti, Phys. Rev. E 68, 046131 (2003).
  17. C. Chatelain, J. Phys. A 36, 10739 (2003).
  18. F. Ricci-Tersenghi, Phys. Rev. E 68, 065104(R) (2003).
  19. E. Lippiello, F. Corberi, and M. Zannetti, e-print cond-mat/0407523.
  20. S. Abriet and D. Karevsky, Eur. Phys. J. B 37, 47 (2004); 41, 79 (2004).
  21. A. Barrat, Phys. Rev. E 57, 3629 (1998).
  22. F. Corberi, C. Castellano, E. Lippiello, and M. Zannetti, Phys. Rev. E 70, 017103 (2004).

  23. dU=2 in the approximate calculations [14, 15, 16] for systems with scalar order parameter shows that there are quantitative features of Rag(t,s) beyond the reach of the best analytical methods presently available.

  24. M. Henkel, M. Pleimling, C. Godrèche and J. M. Luck, Phys. Rev. Lett. 87, 265701 (2001); M. Henkel and M. Pleimling, ibid. 90, 099602 (2003).
  25. M. Henkel, M. Paessens, and M. Pleimling, Phys. Rev. E 69, 056109 (2004).
  26. F. Corberi, E. Lippiello, and M. Zannetti, e-print cond-mat/0506139.
  27. M. Henkel and M. Pleimling, Phys. Rev. E 72, 028104 (2005).
  28. F. Corberi, E. Lippiello, and M. Zannetti, Phys. Rev. E 63, 061506 (2001).
  29. G. F. Mazenko, O. T. Valls, and M. Zannetti, Phys. Rev. B 38, 520 (1988).

  30. In the first set we have omitted s=102, 103, 104 since these values are too close to s=101.

  31. For the modifications in the above argument needed in the large N model see Sec. II A of Ref. [17].

  32. F. Liu and G. F. Mazenko, Phys. Rev. B 44, 9185 (1991).
  33. F. Corberi, E. Lippiello, and M. Zannetti, Phys. Rev. Lett. 90, 099601 (2003).

Outline

Information

Phys. Rev. E 72, 056103– Published 3 November, 2005
  • Received 27 October 2004

© 2005 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation