Advertisement

Pramana

, Volume 64, Issue 6, pp 1075–1085 | Cite as

A sigma-model approach to glassy dynamics

  • Claudio Chamon
  • Leticia F. Cugliandolo
Article

Abstract

In this contribution we review recent progress in understanding fluctuations in the aging process of macroscopic systems, and we propose further tests of these ideas. We discuss how the emergence of a symmetry in aging systems, global timereparametrization invariance, could be responsible for the observed ‘universal’ behavior of local and mesoscopic non-equilibrium fluctuations. We discuss (i) the two-time scaling and functional form of the distribution of local correlations and responses; (ii) the scaling of multi-time correlations and susceptibilities; (iii) how the above can be derived from a random surface effective action; (iv) the behavior of a diverging two-time dependent correlation length; (v) how these ideas apply to off-lattice particle systems.

Keywords

Glasses non-equilibrium dynamics 

PACS Nos

75.10.Nr 75.10.Jm 75.10.Hk 05.30.-d 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1a]
    J P Bouchaud, L F Cugliandolo, J Kurchan and M Mézard, inSpin glasses and random fields edited by A P Young (World Scientific, Singapore, 1998)Google Scholar
  2. [1b]
    L F Cugliandolo, inSlow relaxation and non-equilibrium dynamics in condensed matter edited by J-L Barratet al (Springer-Verlag, 2002), cond-mat/0210312Google Scholar
  3. [2]
    L F Cugliandolo and J Kurchan,Phys. Rev. Lett. 71, 173 (1993)CrossRefADSGoogle Scholar
  4. [3]
    L F Cugliandolo and J Kurchan,J. Phys. A27, 5749 (1994)ADSMathSciNetGoogle Scholar
  5. [4a]
    H Sillescu,J. Non-Crystal. Solids 243, 81 (1999)CrossRefGoogle Scholar
  6. [4b]
    M D Ediger,Annu. Rev. Phys. Chem. 51, 99 (2000)CrossRefGoogle Scholar
  7. [4c]
    E Vidal Russell, N E Israeloff, L E Walther and H Alvarez Gomariz,Phys. Rev. Lett. 81, 1461 (1998)CrossRefADSGoogle Scholar
  8. [4d]
    E Vidal-Russel and N E Israeloff,Nature (London) 408, 695 (2000)CrossRefADSGoogle Scholar
  9. [5a]
    W K Kegel and A V Blaaderen,Science 287, 290 (2000)CrossRefADSGoogle Scholar
  10. [5b]
    E Weeks, J C Crocker, A C Levitt, A Schofield and D A Weitz,Science 287, 627 (2000)CrossRefADSGoogle Scholar
  11. [5c]
    E R Weeks and D A Weitz,Phys. Rev. Lett. 89, 095704 (2002)CrossRefADSGoogle Scholar
  12. [6]
    R E Courtland and E R Weeks,J. Phys. C15, S359 (2003)Google Scholar
  13. [7]
    L Buisson, S Ciliberto and A Garcimartin, cond-mat/0306462Google Scholar
  14. [8a]
    L Cipelletti, H Bissig, V Trappe, P Ballestat and S Mazoyer,J. Phys. C15, S257 (2003)Google Scholar
  15. [8b]
    H Bässig, V Trappe, S Romer and L Cipelletti, cond-mat/0301265Google Scholar
  16. [9a]
    Many articles deal with dynamic heterogeneities in supercooled liquids, see Y Gebremichael, M I Vogel and S C Glotzer,Molecular Simulation,30, 281 (2004)CrossRefGoogle Scholar
  17. [9b]
    For a recent study list of references: Dynamic heterogeneities in the aging Coulomb glass have been studied in A Kolton, D R Grempel and D Domínguez (unpublished); and in an aging Lennard-Jones binary mixture in K Vollmayr-Lee, W Kob, K Binder and A Zippelius,J. Chem. Phys. 116, 5158 (2002)CrossRefADSGoogle Scholar
  18. [10]
    C Chamon, M P Kennett, H E Castillo and L F Cugliandolo,Phys. Rev. Lett. 89, 217201 (2002)CrossRefADSGoogle Scholar
  19. [11]
    H E Castillo, C Chamon, L F Cugliandolo and M P Kennett,Phys. Rev. Lett. 88, 237201 (2002)CrossRefADSGoogle Scholar
  20. [12]
    H E Castillo, C Chamon, L F Cugliandolo, J L Iguain and M P Kennett,Phys. Rev. B68, 134442 (2003)ADSGoogle Scholar
  21. [13]
    C Chamon, P Charbonneau, L F Cugliandolo, D R Reichman and M Sellitto, condmat/0401326Google Scholar
  22. [14]
    E Brézin and J Zinn-Justin,Phys. Rev. B14, 3110 (1976)ADSGoogle Scholar
  23. [15]
    H Sompolinsky,Phys. Rev. Lett. 47, 935 (1981)CrossRefADSGoogle Scholar
  24. [16]
    Vik Dotsenko, M V Fielgel’man and L B Ioffe, Spin-glasses and related problems, inSoviet scientific reviews (Harwood, 1990) Vol. 15Google Scholar
  25. [17]
    S Franz and M Mézard,Europhys. Lett. 26, 209 (1994);Physica A210, 48 (1994)CrossRefGoogle Scholar
  26. [18]
    M P Kennett and C Chamon,Phys. Rev. Lett. 86, 1622 (2001)CrossRefADSGoogle Scholar
  27. [19]
    L F Cugliandolo and J Kurchan,Physica A263, 242 (1999)ADSGoogle Scholar
  28. [20]
    G Semerjian, L F Cugliandolo and A Montanari,J. Stat. Phys. 115, 493 (2004)CrossRefMathSciNetGoogle Scholar
  29. [21]
    L F Cugliandolo, J Kurchan and L Peliti,Phys. Rev. E55, 3898 (1997)ADSGoogle Scholar
  30. [22a]
    Its stationary limit has been studied analytically in the context of thep spin disordered model and mode-coupling theory in S Franz and G Parisi,J. Phys. C12, 6335 (2000);Google Scholar
  31. [22b]
    G Biroli and J-P Bouchaud,Europhys. Lett. 67, 21 (2004), respectivelyCrossRefADSGoogle Scholar
  32. [23]
    Note that there might be a tricky interplay with the thermodynamic limitL » ∞ at least in kinetically facilitated models; see C Toninelli, G Biroli and D S Fisher,Phys. Rev. Lett. 92, 185504 (2004) (unpublished); C Toninelli and G Biroli,J. Stat. Phys. (to appear)CrossRefADSGoogle Scholar
  33. [24]
    E J Gumbel,Statistics of extremes (Columbia University Press, New York, 1958)MATHGoogle Scholar

Copyright information

© Indian Academy of Sciences 2005

Authors and Affiliations

  • Claudio Chamon
    • 1
  • Leticia F. Cugliandolo
    • 2
    • 3
  1. 1.Department of PhysicsBoston UniversityBostonUSA
  2. 2.Laboratoire de Physique ThéoriqueEcole Normale SupérieureParis Cedex 05France
  3. 3.Laboratoire de Physique Théorique et Hautes Energies, JussieuParis Cedex 05France

Personalised recommendations