On the long times, large length scale behaviour of disordered systems

  • Jean-Philippe Bouchaud
  • Marc Mézard
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 492)


We discuss the large scale effective potential for elastic objects in the presence of a random pinning potential. In the static approach, converging analytical results show that the large scale, low temperature free energy landscape consists in a succession of parabolic wells of random depth, matching on singular points where the effective force is discontinuous. These parabolas are themselves subdivided into smaller parabolas, corresponding to the motion of smaller length scales, in a hierarchical manner. Consequences for the dynamics of these pinned objects are underlined, and compared to the mean field theory of aging effects.


Energy Landscape Flux Line Effective Force Large Length Scale Replica Symmetry 
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  1. [1]
    D. S. Fisher, M.P.A. Fisher, D. A. Huse, Phys Rev B 43, 130 (1991)CrossRefADSGoogle Scholar
  2. [2]
    G. Blatter, M. V. Feigel’man, V. B. Geshkenbin, A. I. Larkin and V. M. Vinokur, Rev. Mod. Phys. 66 (1994) 4.CrossRefGoogle Scholar
  3. [3]
    for a recent review, see e.g. M. Kardar, D. Ertas, in ’scale Invariance, Interfaces and Non-equilibrium dynamics’, NATO-ASI (1995), Kluwer., M. Kardar, ‘Lectures on directed paths in random media’, Les Houches Summer School on ‘Fluctuating geometries in Statistical Mechanics and Field Theory’, in press.Google Scholar
  4. [4]
    T. Nattermann and P. Rujan, Int. J. Mod. Phys. B3 (1989) 1597ADSGoogle Scholar
  5. [4a]
    T. Natterman and J. Villain, Phase transitions 11 (1988) 5CrossRefGoogle Scholar
  6. [5]
    R. Vergne, J. C. Cotillard, J.L. Porteseil, Rev. Phys. Appl. 16 449 (1981).Google Scholar
  7. [6]
    L. Néel, Cahier de la Physique 12 (1942) and 13 (1943)Google Scholar
  8. [7]
    H. Fukuyama and P. A. Lee, Phys. Rev. B 17, 535 (1978).ADSGoogle Scholar
  9. [8]
    D. S. Fisher, Phys. Rev. B 31, 7233 (1985).ADSGoogle Scholar
  10. [9]
    T. Halpin-Healey and Y.C. Zhang; Phys. Rep. 254 (1995) 217CrossRefADSGoogle Scholar
  11. [10]
    G. Parisi, J. Phys. France 51 1595 (1990)MathSciNetCrossRefGoogle Scholar
  12. [11]
    M. Mézard, J. Phys. France 51 1831 (1990)CrossRefGoogle Scholar
  13. [12]
    T. Hwa, D. S. Fisher, Phys. Rev. B 49 3136 (1994)ADSGoogle Scholar
  14. [13]
    L. Balents, J.P. Bouchaud and M. Mézard, cond-mat/9601137, to appear in J. Physique (August 1996).Google Scholar
  15. [14]
    M. Mézard, G. Parisi, J. Physique I 1 809 (1991); J.Phys. A23 L1229 (1990)CrossRefADSGoogle Scholar
  16. [15]
    J.P. Bouchaud, M. Mézard, J. Yedidia, Phys. Rev B 46 14 686 (1992)CrossRefGoogle Scholar
  17. [16]
    S. E. Korshunov, Phys. Rev. B 48, 3969 (1993)CrossRefADSGoogle Scholar
  18. [16a]
    T. Giamarchi, P. Le Doussal, Phys. Rev. B 52 1242 (1995)ADSGoogle Scholar
  19. [17]
    J.P. Bouchaud, M. Mézard, G. Parisi, Phys. Rev. E 52 (1995) 3656ADSGoogle Scholar
  20. [18]
    D.S. Fisher, Phys. Rev. Lett. 56 (1986) 1964CrossRefADSGoogle Scholar
  21. [18a]
    L. Balents, D. S. Fisher, Phys. Rev. B 48 (1993) 5949ADSGoogle Scholar
  22. [19]
    M. Mézard, G. Parisi, M.A. Virasoro, “Spin Glass Theory and Beyond”, (World Scientific, Singapore 1987)zbMATHGoogle Scholar
  23. [20]
    J. M. Burgers, ‘The Non-Linear Diffusion Equation’, D. Reidel Pub. Co. (1974)Google Scholar
  24. [21]
    S. Kida, J. Fluid. Mech. 93 (1979) 337zbMATHCrossRefADSMathSciNetGoogle Scholar
  25. [22]
    J.P. Bouchaud, M. Mézard, preprint cond-mat 9607006Google Scholar
  26. [23]
    J.P. Bouchaud, J. Physique I (Paris) 2 (1992) 1705ADSCrossRefGoogle Scholar
  27. [23a]
    J.P. Bouchaud, D.S. Dean, J. Physique I (Paris) 5 (1995) 265. See also: C. Monthus, J.P. Bouchaud, preprint cond-mat 9601012, submitted to J. Phys. A.ADSCrossRefGoogle Scholar
  28. [24]
    E. Vincent, J. Hammann, M. Ocio, p. 207 in “Recent Progress in Random Magnets”, D.H. Ryan Editor, (World Scientific Pub. Co. Pte. Ltd, Singapore 1992)Google Scholar
  29. [25]
    E. Vincent, J. Hammann, M. Ocio, J. P. Bouchaud, L. Cugliandolo, this volume.Google Scholar
  30. [26]
    F. Alberici, P. Doussineau, A. Levelut, preprint.Google Scholar
  31. [27]
    P.C. Martin, E.D. Siggia and H.A. Rose; Phys. Rev. A8 (1978) 423ADSGoogle Scholar
  32. [27a]
    C. de Dominicis, L. Peliti, Phys. Rev. B18 (1978) 353.ADSGoogle Scholar
  33. [28]
    H. Sompolinsky and A. Zippelius, Phys. Rev. Lett. 47 (1981) 359; Phys. Rev. A 25 (1982) 6860.CrossRefADSGoogle Scholar
  34. [29]
    H. Kinzelbach and H. Horner, J. Phys. I France 3, 1329 (1993); J. Phys. I France 3, 1901 (1993)CrossRefGoogle Scholar
  35. [30]
    L. F. Cugliandolo and J. Kurchan, Phys. Rev. Lett. 71 (1993) 173CrossRefADSGoogle Scholar
  36. [31]
    S. Franz and M. Mézard, Europhys. Lett. 26 (1994) 209; Physica A209 (1994) 1CrossRefADSGoogle Scholar
  37. [32]
    L. F. Cugliandolo and J. Kurchan, J. Phys. A27 (1994) 5749ADSMathSciNetGoogle Scholar
  38. [33]
    L. F. Cugliandolo and P. Le Doussal; Phys. Rev. E53, 1525 (1996).ADSGoogle Scholar
  39. [33a]
    L. F. Cugliandolo, J. Kurchan and P. Le Doussal; Phys. Rev. Lett. 76, 2390 (1996).CrossRefADSGoogle Scholar
  40. [34]
    A. Barrat and M. Mézard; J. Phys. I (France) 5 (1995) 941CrossRefGoogle Scholar
  41. [35]
    J. Kurchan and L. Laloux; J. Phys. A29, 1929 (1996)ADSMathSciNetGoogle Scholar
  42. [36]
    F. Ritort, Phys. Rev. Lett. 75 (1995) 1190CrossRefADSGoogle Scholar
  43. [36a]
    S. Franz and F. Ritort, preprint cond-mat/9508133; C. Godrèche, J.P. Bouchaud and M. Mézard, J. Phys. A28 (1996) L603Google Scholar
  44. [37]
    A. Barrat, R. Burioni and M. Mézard, J. Phys. A29 (1996) 1311ADSGoogle Scholar
  45. [38]
    For reviews, see W. Götze, in Liquids, freezing and glass transition, Les Houches 1989, JP Hansen, D. Levesque, J. Zinn-Justin Editors, North Holland. see also W. Götze, L. Sjögren, Rep. Prog. Phys. 55 (1992) 241CrossRefADSGoogle Scholar
  46. [39]
    S. Franz and J. Hertz, Phys. Rev. Lett. 74 (1995) 2114CrossRefADSGoogle Scholar
  47. [40]
    J-P Bouchaud, L. F. Cugliandolo, J. Kurchan and M. Mézard; Physica A226, 243 (1996)ADSGoogle Scholar
  48. [41]
    M. Feigel’man, L. Ioffe, Z. Phys. B 51 (1983) 237.CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Jean-Philippe Bouchaud
    • 1
  • Marc Mézard
    • 2
  1. 1.Service de Physique de l’État CondenséCentre d’études de Saclay, Orme des MerisiersGif-sur-Yvette CedexFrance
  2. 2.Laboratoire de Physique Théorique de l’ENSParis Cedex 05France

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