Damage spreading transition in glasses: A probe for the ruggedness of the configurational landscape

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 60, Issue 4, 1999, Pages 3646-3665

  Heerema, M ^a   Ritort, F ^b  

^a UNIVERSITY OF AMSTERDAM   (Netherlands)

^b UNIVERSITY OF BARCELONA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE;

EID: 0008972641     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.60.3646     Document Type: Article

References (53)

1. Proceedings of the XIV Sitges Conference, Complex Behavior of Glassy Systems, edited by M. Rubí and C. Perez-Vicente (Springer-Verlag, Berlin, 1997).
2. C. A. Angell, Science 267, 1924 (1995).
3. J. P. Bouchaud, L. F. Cugliandolo, J. Kurchan, and M. Mezard, in Spin Glasses and Random Fields, edited by A. P. Young (World Scientific, Singapore, 1997).
4. J. H. Gibbs and E. A. Di Marzio, J. Chem. Phys. 28, 373 (1958)
5. J. Chem. Phys.G. Adams and J. H. Gibbs, 43, 139 (1965).
6. T. R. Kirkpatrick and D. Thirumalai, Phys. Rev. B 36, 5388 (1987)
7. Phys. Rev. BT. R. Kirkpatrick and P. G. Wolyness, 36, 8552 (1987).
8. W. Götze, Liquid, Freezing and the Glass Transition, Les Houches, edited by J. P. Hansen, D. Levesque, and J. Zinn-Justin (North-Holland, Amsterdam, 1989), p. 287.
9. Exponentially large means that the number of metastable states grows like (Formula presented), where (Formula presented) is a constant and N denotes the size or volume of the system.
10. E. Marinari, G. Parisi, and F. Ritort, J. Phys. A 27, 7615 (1994).
11. E. Marinari, G. Parisi, and F. Ritort, J. Phys. A 27, 7647 (1994).
12. J. P. Bouchaud and M. Mezard, J. Phys. I 4, 1109 (1994).
13. F. Ritort, Phys. Rev. Lett. 75, 1190 (1995).
14. L. L. Bonilla, F. G. Padilla, and F. Ritort, Physica A 250, 315 (1998).
15. S. Ciuchi and F. De Pascuale, Nucl. Phys. B 300, 31 (1998)
16. L. F. Cugliandolo and D. S. Dean, J. Phys. A 28, 213 (1995).
17. J. Kurchan and L. Laloux, J. Phys. A 29, 1929 (1996).
18. S. A. Kauffman, J. Theor. Biol. 22, 437 (1969).
19. B. Derrida and Y. Pomeau, Europhys. Lett. 1, 46 (1986)
20. M. Creutz, Ann. Phys. (N.Y.) 167, 62 (1986)
21. H. E. Stanley, D. Stauffer, J. Kertesz, and H. J. Hermann, Phys. Rev. Lett. 59, 2326 (1987).
22. B. Derrida and G. Weisbuch, Europhys. Lett. 4, 657 (1987).
23. B. Derrida, Phys. Rep. 184, 207 (1989).
24. A. Coniglio, L. De Arcangelis, H. J. Herrmann, and N. Jan, Europhys. Lett. 8, 315 (1989).
25. G. Parisi, Nucl. Phys. B 180, 378 (1981).
26. O. Martin, Nucl. Phys. B 251, 425 (1985)
27. O. MartinJ. Stat. Phys. 41, 249 (1985).
28. E. Domany and W. Kinzel, Phys. Rev. Lett. 53, 311 (1984)
29. Phys. Rev. Lett.M. L. Martins, H. F. Verona de Resende, C. Tsallis, and A. C. N. de Magalhaes, 66, 2045 (1991).
30. H. Hinrichsen and E. Domany, Phys. Rev. E 56, 94 (1997).
31. T. Vojta, Phys. Rev. E 55, 5157 (1997).
32. I. Graham, E. Hernandez-Garcia, and M. Grant, Phys. Rev. E 49, R4763 (1994).
33. D. Stariolo, Philos. Mag. B 77, 671 (1998).
34. For a recent review, see W. Kob, e-print cond-mat/9809268.
35. V. Loreto, M. Serva, and A. Vulpiani, Int. J. Mod. Phys. B 12, 225 (1998).
36. A. Crisanti, H. Horner, and H.-J. Sommers, Z. Phys. B 92, 257 (1993).
37. A. Crisanti and H. J. Sommers, J. Phys. I 5, 805 (1995).
38. A useful collection of results and formulas can be found in A. Barrat, Ph. D. thesis, Université Paris VI (1996)
39. A. Barrate-print cond-mat/9701031.
40. M. Heerema and F. Ritort, J. Phys. A 31, 8423 (1998).
41. L. F. Cugliandolo, J. Kurchan, P. Le Doussal, and L. Peliti, Phys. Rev. Lett. 78, 350 (1997).
42. L. F. Cugliandolo and J. Kurchan, Phys. Rev. Lett. 71, 173 (1993).
43. S. Franz, E. Marinari, and G. Parisi, J. Phys. A 28, 5437 (1995).
44. Let us note that these expansions are only valid in the time sector (Formula presented) so the coefficients (Formula presented) (Formula presented) and (Formula presented) are not symmetric under exchange of the subindices (Formula presented).
45. Th. M. Nieuwenhuizen, Phys. Rev. Lett. 74, 4289 (1995).
46. In this section our discussion is only valid for (Formula presented), where there exists a stationary Boltzmann distribution.
47. A. Crisanti and H. Sompolinsky, Phys. Rev. A 36, 4922 (1987).
48. This expression does not hold for (Formula presented) but is surprisingly good for (Formula presented) (numerically within one part in a thousand). So we suspect that for (Formula presented) this is the exact result.
49. H. Heinrichsen, S. Weitz and E. Domany, J. Stat. Phys. 18, 617 (1997).
50. J. Bernasconi, J. Phys. (Paris) 48, 559 (1987).
51. T. R. Kirkpatrick and D. Thirumalai, J. Phys. A 22, L149 (1989).
52. G. Migliorini and F. Ritort, J. Phys. A 27, 7669 (1994).
53. A. J. Bray and M. A. Moore, J. Phys. C 13, L469 (1980).