Mode-coupling approximations, glass theory and disordered systems

Physica A: Statistical Mechanics and its Applications

Volumn 226, Issue 3-4, 1996, Pages 243-273

  Bouchaud, Jean Philippe ^a   Cugliandolo, Leticia ^a   Kurchan, Jorge ^b   Mézard, Marc ^b  

^a CEA SACLAY   (France)

^b LABORATOIRE DE PHYSIQUE STATISTIQUE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 30244435648     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/0378-4371(95)00423-8     Document Type: Article

References (70)

1. For a review, see e.g., W.D. McComb, The Physics of Fluid Turbulence (Oxford Science Publications, Oxford, 1990); R.H. Kraichnan and S. Chen, Physica D 37 (1989) 160.
2. For a review, see e.g., W.D. McComb, The Physics of Fluid Turbulence (Oxford Science Publications, Oxford, 1990); R.H. Kraichnan and S. Chen, Physica D 37 (1989) 160.
3. T. Halpin-Healey and Y.C. Zhang, Phys. Rep. 254 (1995) 217.
4. For reviews, see W. Götze, in: Liquids, Freezing and Glass Transition, JP Hansen, D. Levesque, J. Zinn-Justin, eds., Les Houches, 1989 (North Holland, Amsterdam, 1989); see also W. Götze, L. Sjögren, Rep. Prog. Phys. 55 (1992) 241.
5. For reviews, see W. Götze, in: Liquids, Freezing and Glass Transition, JP Hansen, D. Levesque, J. Zinn-Justin, eds., Les Houches, 1989 (North Holland, Amsterdam, 1989); see also W. Götze, L. Sjögren, Rep. Prog. Phys. 55 (1992) 241.
6. There are so many papers using this technique that we only give a very subjective selection of them: R. Kraichnan, J. Fluid. Mech. 5 497 (1959); K. Kawasaki, Ann. Phys. 61 (1970) 1; H. Van Beijeren, R. Kutner and H. Spohn, Phys. Rev. Lett 54 (1985) 2026. In the context of the Kardar-Parisi-Zhang equation, see J. Krug, Phys. Rev. A 36 (1987) 5465; J.P. Bouchaud and ME. Cates, Phys. Rev. E 47 (1993) R1455; Erratum E48 (1993) 635; M.A. Moore, T. Blum, J. Doherty, M. Marsili, J.P. Bouchaud and Ph. Claudin, Phys. Rev. Lett. 74 (1995) 4257. For related ideas, see also M. Schwartz and S.F. Edwards, Europhys. Lett 20 (1992) 301; T. Blum and A.J. McKane, cond-mat 9505038.
7. There are so many papers using this technique that we only give a very subjective selection of them: R. Kraichnan, J. Fluid. Mech. 5 497 (1959); K. Kawasaki, Ann. Phys. 61 (1970) 1; H. Van Beijeren, R. Kutner and H. Spohn, Phys. Rev. Lett 54 (1985) 2026. In the context of the Kardar-Parisi-Zhang equation, see J. Krug, Phys. Rev. A 36 (1987) 5465; J.P. Bouchaud and ME. Cates, Phys. Rev. E 47 (1993) R1455; Erratum E48 (1993) 635; M.A. Moore, T. Blum, J. Doherty, M. Marsili, J.P. Bouchaud and Ph. Claudin, Phys. Rev. Lett. 74 (1995) 4257. For related ideas, see also M. Schwartz and S.F. Edwards, Europhys. Lett 20 (1992) 301; T. Blum and A.J. McKane, cond-mat 9505038.
8. There are so many papers using this technique that we only give a very subjective selection of them: R. Kraichnan, J. Fluid. Mech. 5 497 (1959); K. Kawasaki, Ann. Phys. 61 (1970) 1; H. Van Beijeren, R. Kutner and H. Spohn, Phys. Rev. Lett 54 (1985) 2026. In the context of the Kardar-Parisi-Zhang equation, see J. Krug, Phys. Rev. A 36 (1987) 5465; J.P. Bouchaud and ME. Cates, Phys. Rev. E 47 (1993) R1455; Erratum E48 (1993) 635; M.A. Moore, T. Blum, J. Doherty, M. Marsili, J.P. Bouchaud and Ph. Claudin, Phys. Rev. Lett. 74 (1995) 4257. For related ideas, see also M. Schwartz and S.F. Edwards, Europhys. Lett 20 (1992) 301; T. Blum and A.J. McKane, cond-mat 9505038.
9. There are so many papers using this technique that we only give a very subjective selection of them: R. Kraichnan, J. Fluid. Mech. 5 497 (1959); K. Kawasaki, Ann. Phys. 61 (1970) 1; H. Van Beijeren, R. Kutner and H. Spohn, Phys. Rev. Lett 54 (1985) 2026. In the context of the Kardar-Parisi-Zhang equation, see J. Krug, Phys. Rev. A 36 (1987) 5465; J.P. Bouchaud and ME. Cates, Phys. Rev. E 47 (1993) R1455; Erratum E48 (1993) 635; M.A. Moore, T. Blum, J. Doherty, M. Marsili, J.P. Bouchaud and Ph. Claudin, Phys. Rev. Lett. 74 (1995) 4257. For related ideas, see also M. Schwartz and S.F. Edwards, Europhys. Lett 20 (1992) 301; T. Blum and A.J. McKane, cond-mat 9505038.
10. There are so many papers using this technique that we only give a very subjective selection of them: R. Kraichnan, J. Fluid. Mech. 5 497 (1959); K. Kawasaki, Ann. Phys. 61 (1970) 1; H. Van Beijeren, R. Kutner and H. Spohn, Phys. Rev. Lett 54 (1985) 2026. In the context of the Kardar-Parisi-Zhang equation, see J. Krug, Phys. Rev. A 36 (1987) 5465; J.P. Bouchaud and ME. Cates, Phys. Rev. E 47 (1993) R1455; Erratum E48 (1993) 635; M.A. Moore, T. Blum, J. Doherty, M. Marsili, J.P. Bouchaud and Ph. Claudin, Phys. Rev. Lett. 74 (1995) 4257. For related ideas, see also M. Schwartz and S.F. Edwards, Europhys. Lett 20 (1992) 301; T. Blum and A.J. McKane, cond-mat 9505038.
11. There are so many papers using this technique that we only give a very subjective selection of them: R. Kraichnan, J. Fluid. Mech. 5 497 (1959); K. Kawasaki, Ann. Phys. 61 (1970) 1; H. Van Beijeren, R. Kutner and H. Spohn, Phys. Rev. Lett 54 (1985) 2026. In the context of the Kardar-Parisi-Zhang equation, see J. Krug, Phys. Rev. A 36 (1987) 5465; J.P. Bouchaud and ME. Cates, Phys. Rev. E 47 (1993) R1455; Erratum E48 (1993) 635; M.A. Moore, T. Blum, J. Doherty, M. Marsili, J.P. Bouchaud and Ph. Claudin, Phys. Rev. Lett. 74 (1995) 4257. For related ideas, see also M. Schwartz and S.F. Edwards, Europhys. Lett 20 (1992) 301; T. Blum and A.J. McKane, cond-mat 9505038.
12. There are so many papers using this technique that we only give a very subjective selection of them: R. Kraichnan, J. Fluid. Mech. 5 497 (1959); K. Kawasaki, Ann. Phys. 61 (1970) 1; H. Van Beijeren, R. Kutner and H. Spohn, Phys. Rev. Lett 54 (1985) 2026. In the context of the Kardar-Parisi-Zhang equation, see J. Krug, Phys. Rev. A 36 (1987) 5465; J.P. Bouchaud and ME. Cates, Phys. Rev. E 47 (1993) R1455; Erratum E48 (1993) 635; M.A. Moore, T. Blum, J. Doherty, M. Marsili, J.P. Bouchaud and Ph. Claudin, Phys. Rev. Lett. 74 (1995) 4257. For related ideas, see also M. Schwartz and S.F. Edwards, Europhys. Lett 20 (1992) 301; T. Blum and A.J. McKane, cond-mat 9505038.
13. There are so many papers using this technique that we only give a very subjective selection of them: R. Kraichnan, J. Fluid. Mech. 5 497 (1959); K. Kawasaki, Ann. Phys. 61 (1970) 1; H. Van Beijeren, R. Kutner and H. Spohn, Phys. Rev. Lett 54 (1985) 2026. In the context of the Kardar-Parisi-Zhang equation, see J. Krug, Phys. Rev. A 36 (1987) 5465; J.P. Bouchaud and ME. Cates, Phys. Rev. E 47 (1993) R1455; Erratum E48 (1993) 635; M.A. Moore, T. Blum, J. Doherty, M. Marsili, J.P. Bouchaud and Ph. Claudin, Phys. Rev. Lett. 74 (1995) 4257. For related ideas, see also M. Schwartz and S.F. Edwards, Europhys. Lett 20 (1992) 301; T. Blum and A.J. McKane, cond-mat 9505038.
14. For an enlightening introduction to the experimental controversy, see the series of Comments in Phys. Rev. E: X.C. Zeng, D. Kivelson and G. Tarjus, Phys. Rev. E 50 (1994) 1711; P.K. Dixon, N. Menon and S.R. Nagel, Phys. Rev. E 50 (1994) 1717; H.Z. Cummins and G. Li, Phys. Rev. E 50 (1994) 1720, and references therein, in particular H.Z. Cummins, W.M. Du, M. Fuchs, W. Götze, S. Hildebrand, A. Latz, G. Li and N.J. Tao, Phys. Rev. E 47 (1993) 4223.
15. For an enlightening introduction to the experimental controversy, see the series of Comments in Phys. Rev. E: X.C. Zeng, D. Kivelson and G. Tarjus, Phys. Rev. E 50 (1994) 1711; P.K. Dixon, N. Menon and S.R. Nagel, Phys. Rev. E 50 (1994) 1717; H.Z. Cummins and G. Li, Phys. Rev. E 50 (1994) 1720, and references therein, in particular H.Z. Cummins, W.M. Du, M. Fuchs, W. Götze, S. Hildebrand, A. Latz, G. Li and N.J. Tao, Phys. Rev. E 47 (1993) 4223.
16. For an enlightening introduction to the experimental controversy, see the series of Comments in Phys. Rev. E: X.C. Zeng, D. Kivelson and G. Tarjus, Phys. Rev. E 50 (1994) 1711; P.K. Dixon, N. Menon and S.R. Nagel, Phys. Rev. E 50 (1994) 1717; H.Z. Cummins and G. Li, Phys. Rev. E 50 (1994) 1720, and references therein, in particular H.Z. Cummins, W.M. Du, M. Fuchs, W. Götze, S. Hildebrand, A. Latz, G. Li and N.J. Tao, Phys. Rev. E 47 (1993) 4223.
17. For an enlightening introduction to the experimental controversy, see the series of Comments in Phys. Rev. E: X.C. Zeng, D. Kivelson and G. Tarjus, Phys. Rev. E 50 (1994) 1711; P.K. Dixon, N. Menon and S.R. Nagel, Phys. Rev. E 50 (1994) 1717; H.Z. Cummins and G. Li, Phys. Rev. E 50 (1994) 1720, and references therein, in particular H.Z. Cummins, W.M. Du, M. Fuchs, W. Götze, S. Hildebrand, A. Latz, G. Li and N.J. Tao, Phys. Rev. E 47 (1993) 4223.
18. R. Kraichnan, J. Fluid. Mech. 7 (1961) 124.
19. A. Bray, Phys. Rev. Lett. 32 (1974) 1413. For recent developments in the context of disordered systems, see M. Mézard and A.P. Young, Europhys. Lett. 18 (1992) 653; M. Mézard and R. Monasson, Phys. Rev. B 50 (1994) 7199.
20. A. Bray, Phys. Rev. Lett. 32 (1974) 1413. For recent developments in the context of disordered systems, see M. Mézard and A.P. Young, Europhys. Lett. 18 (1992) 653; M. Mézard and R. Monasson, Phys. Rev. B 50 (1994) 7199.
21. A. Bray, Phys. Rev. Lett. 32 (1974) 1413. For recent developments in the context of disordered systems, see M. Mézard and A.P. Young, Europhys. Lett. 18 (1992) 653; M. Mézard and R. Monasson, Phys. Rev. B 50 (1994) 7199.
22. C.Y. Mou and P.B. Weichman, Phys. Rev. Lett. 70 (1993) 1101.
23. S. Franz and J. Hertz, Phys. Rev. Lett. 74 (1995) 2114.
24. T.R. Kirkpatrick and D. Thirumalai, J. Phys. A 22 (1989) L149.
25. J.P. Bouchaud and M. Mézard, J. Phys. I (France) 4 (1994) 1109; E. Marinari, G. Parisi and F. Ritort, J. Phys. A 27 (1994) 7615; J. Phys. A 27 (1994) 7647.
26. J.P. Bouchaud and M. Mézard, J. Phys. I (France) 4 (1994) 1109; E. Marinari, G. Parisi and F. Ritort, J. Phys. A 27 (1994) 7615; J. Phys. A 27 (1994) 7647.
27. J.P. Bouchaud and M. Mézard, J. Phys. I (France) 4 (1994) 1109; E. Marinari, G. Parisi and F. Ritort, J. Phys. A 27 (1994) 7615; J. Phys. A 27 (1994) 7647.
28. L.F. Cugliandolo, J. Kurchan, G. Parisi and F. Ritort, Phys. Rev. Lett. 74 (1995) 1012; P. Chandra, L. Ioffe and D. Sherrington, cond-mat 9502018; P. Chandra, M. Feigelmann and L. Ioffe, preprint cond-mat 9509022.
29. L.F. Cugliandolo, J. Kurchan, G. Parisi and F. Ritort, Phys. Rev. Lett. 74 (1995) 1012; P. Chandra, L. Ioffe and D. Sherrington, cond-mat 9502018; P. Chandra, M. Feigelmann and L. Ioffe, preprint cond-mat 9509022.
30. L.F. Cugliandolo, J. Kurchan, G. Parisi and F. Ritort, Phys. Rev. Lett. 74 (1995) 1012; P. Chandra, L. Ioffe and D. Sherrington, cond-mat 9502018; P. Chandra, M. Feigelmann and L. Ioffe, preprint cond-mat 9509022.
31. E. Vincent, J. Hammann and M. Ocio, in: Recent Progress in Random Magnets, D.H. Ryan, ed. (World Scientific, Singapore, 1992) p. 207.
32. L.C.E. Struik, Physical Aging in Amorphous Polymers and Other Materials (Elsevier, Houston, 1978).
33. J.P. Bouchaud, J. Phys. I (France) 2 (1992) 1705; J.P. Bouchaud and D.S. Dean, J. Phys. I (France) 5 (1995) 265.
34. J.P. Bouchaud, J. Phys. I (France) 2 (1992) 1705; J.P. Bouchaud and D.S. Dean, J. Phys. I (France) 5 (1995) 265.
35. L.F. Cugliandolo and J. Kurchan, Phys. Rev. Lett. 71 (1993) 173;
36. J. Phys. A 27 (1994) 5749.
37. S. Franz and M. Mézard, Europhys. Lett. 26 (1994) 209; Physica A 209 (1994) 1.
38. S. Franz and M. Mézard, Europhys. Lett. 26 (1994) 209; Physica A 209 (1994) 1.
39. L.F. Cugliandolo and P. Le Doussal, Large time off-equilibrium dynamics of a particle diffusing in a random potential, cond-mat 9505112, Phys. Rev. E, to be published; L.F. Cugliandolo, J. Kurchan and P. Le Doussal, preprint cond-mat 9509009.
40. L.F. Cugliandolo and P. Le Doussal, Large time off-equilibrium dynamics of a particle diffusing in a random potential, cond-mat 9505112, Phys. Rev. E, to be published; L.F. Cugliandolo, J. Kurchan and P. Le Doussal, preprint cond-mat 9509009.
41. M. Mézard, G. Parisi and M.A. Virasoro, Spin Glass Theory and Beyond, ch. VI (World Scientific, Singapore, 1987).
42. G. Eynick, Phys. Rev. E 49 (1994) 3990.
43. J. Bernasconi, J. Physique 48 (1987) 559.
44. D.J. Amit and D.V. Roginsky, J. Phys. A 12 (1979) 689.
45. J.P. Doherty, A.J. Bray, J.M. Kim and M.A. Moore, Phys. Rev. Lett. 72 (1994) 2041.
46. For a review, see A.J. Bray, Adv. in Phys. 43 (1994) 357.
47. M. Campellone et al., in preparation.
48. S. Gauthier, M.E. Brachet, J.N. Fournier, J. Phys. A 14 (1981) 2969.
49. H.J. Sommers and K.H. Fischer, Z. Phys. B 58 (1985) 125.
50. T.R. Kirkpatrick and D. Thirumalai, Phys. Rev. B 36 (1987) 5388.
51. H. Kinzelbach and H. Horner, J. Phys. I (France) 3 (1993) 1329; J. Phys. I (France) 3 (1993) 1901.
52. H. Kinzelbach and H. Horner, J. Phys. I (France) 3 (1993) 1329; J. Phys. I (France) 3 (1993) 1901.
53. T.R. Kirkpatrick, D. Thirumalai and P.G. Wolynes, Phys. Rev. A 40 (1989) 1045, and references therein.
54. G. Parisi, Slow dynamics in glasses, cond-mat 941115; cond-mat 9412034.
55. M. Mézard, G. Parisi, J. Physique I 1 809 (1991); J. Phys. A 23 (1990) L1229.
56. M. Mézard, G. Parisi, J. Physique I 1 809 (1991); J. Phys. A 23 (1990) L1229.
57. For a review, see the interesting series of papers in Science 267 (1995) 1924.
58. H. Bassler, Phys. Rev. Lett. 58 (1987) 767;
59. V. Arkhipov, H. Bassler, Phys. Rev. E 52 (1995) 1227, and references therein.
60. T. Odagaki, J. Matsui and Y. Hiwatari, Physica A 204 (1994) 464.
61. S. Gomi and F. Yonezawa, 74 (1995) 4125.
62. A. Barrat and M. Mézard, J. Phys. I (France) 5 (1995) 941.
63. J.P. Bouchaud, A. Comtet and C. Monthus, On a dynamical model of glasses, cond-mat 9506027, J. Physique I (1995), to appear; C. Monthus and J.P. Bouchaud, in preparation.
64. Such a program was attempted, in a rather formal way, in: L. Sjögren, Z. Phys. B 74 (1989) 353.
65. E. Gozzi, Phys. Rev. D 30 (1984) 1218.
66. J. Zinn Justin, "Quantum Field Theory and Critical Phenomena" (Clarendon Press, Oxford, 1989).
67. J. Kurchan, J. Phys. I (France) I (1992) 1333.
68. P.C. Martin, E.D. Siggia and H.A. Rose, Phys. Rev. A 8 (1978) 423.
69. C. de Dominicis and L. Peliti, Phys. Rev. B 18 (1978) 353.
70. L.F. Cugliandolo and J. Kurchan, Philos. Mag. B 71 (1995) 50.