Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-28T02:30:13.506Z Has data issue: false hasContentIssue false
  • English
  • Français

Aging and Glassy Dynamics in Complex Systems: Some Theoretical Ideas

Published online by Cambridge University Press:  03 September 2012

Jean-Philippe Bouchaud
Jean-Philippe Bouchaud*
Affiliation:
Service de Physique de l'Etat Condensé, Commissariat à l'Energie Atomique, Orme des Merisiers, 91191 Gif-sur-Yvette CEDEX, France
Get access

Abstract

We discuss some recent experimental results on the non-stationary dynamics of spin-glasses, which serves as an excellent laboratory for other complex systems. Inspired from Parisi's mean-field solution, we propose that the dynamics of these systems can be though of as a random walk in phase space, between traps characterized by trapping time distribution decaying as a power law. The average exploration time diverges in the spin-glass phase, naturally leading to time-dependent dynamics with a charateristic time scale fixed by the observation time tw itself (aging). By the same token, we find that the correlation function (or the magnetization) decays as a stretched exponential at small times t ≪ tw crossing over to power-law decay at large times t ≫ tw. Finally, we discuss recent speculations on the relevance of these concepts to real glasses, where quenched disorder is a priori absent. Keywords: Aging, slow dynamics, spin-glasses, glasses.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 367: Symposium P – Fractal Aspects of Materials , 1994 , 347
Copyright
Copyright © Materials Research Society 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] for a review, see: Vincent, E., Hammann, J., Ocio, M., p. 207 in “Recent Progress in Random Magnets”, Ryan, D.H. Editor, (World Scientific Pub. Co. Pte. Ltd, Singapore 1992)Google Scholar
[2] Struick, L.C.E., “Physical Aging in Amorphous Polymers and Other Materials” (Else-vier, Houston, 1978)Google Scholar
[3] Cugliandolo, L., Kurchan, J., Phys. Rev. Lett. 71 173 (1993), S. Franz, M. Mezard, Europhys. Lett. 26 209 (1994), Physica A209 1 (1994), L. Cugliandolo, J. Kurchan, J. Phys. A 27 5749 (1994), H. Rieger, preprint (cond-mat, October 94)Google Scholar
[4] Fisher, D.S, Huse, D.A., Phys. Rev. Lett 56, 1601 (1986), Phys. Rev. B 38, 373 (1988), G.J. Koper, H.J. Hilhorst, J. Physique (France) 49 429 (1988)Google Scholar
[5] Bray, A. J., Theory of phase ordering kinetics, to appear in Adv. Physics (1994)Google Scholar
[6] a- Bouchaud, J.P., J. Physique I (France) 2, 1705 (1992), b- J.P. Bouchaud, E. Vincent, J. Hammann, J. Physique I (France) 4, 139 (1994)Google Scholar
[7] Mezard, M., Parisi, G., Virasoro, M.A., “Spin Glass Theory and Beyond”, (World Scientific, Singapore 1987), B. Derrida, Phys. Rev. B 24, 2613 (1981), D.J. Gross, M. Mdzard, Nucl. Phys. B240 431 (1984).Google Scholar
[8] Bouchaud, J.P., Georges, A., Phys. Rep. 195 127 (1990)Google Scholar
[9] Bouchaud, J.P., Dean, D.S., ‘Aging on Parisi's tree’, submitted to J. Physique IGoogle Scholar
[10] Hammann, J., Lederman, M., Ocio, M., Orbach, R., Vincent, E., Physica A 185, 278 (1992), F. Lefloch, J. Hammann, M. Ocio, E. Vincent, Europhys. Lett 18, 647 (1992)Google Scholar
[11] Alers, G. B., Weissmann, M. B., Isrealoff, N.E., Phys. Rev. B 46, 507 (1992), M. B. Weissmann, N.E. Isrealoff, G. B. Alers, Journal of Magn. Magn. Mat. 114, 87 (1992), and M. B. Weissmann, Rev. Mod. Phys., July 1993.Google Scholar
[12] Mézard, M., Parisi, G., J. Physique I 1 809 (1991), J.P. Bouchaud, M. Mezard, J. Yedidia, Phys. Rev B 46 14 686 (1992)Google Scholar
[13] Bouchaud, J.P., Mezard, M. J. Phys. I France 4 1109 (1994), E. Marinari, G. Parisi, F. Ritort, Replica Field Theory for Deterministic Models: Binary Sequences with Low Autocorrelation I and II preprint cond-mat/9406074, L. F. Cugliandolo, I. Kurchan, G.Parisi, F.Ritort, Matrix Models as solvable Glass Models to appear in Phys. Rev. Lett., S. Franz, J. Hertz, Glassy transition and aging in a model without disorder preprint cond-mat/9408075, T. Blum, J. Doherty, M.A. Moore, J.P. Bouchaud, P. Claudin, Glassy solutions of the KPZ equation, submitted to Phys. Rev. Lett.Google Scholar
[14] Kirkpatrick, T., Thirumalai, D., J. Phys. A 22 L149 (1989)Google Scholar
[15] Odagaki, T., Matsui, J., Hiwatari, Y., Physica A 204 464 (1994).Google Scholar
[16] Doussineau, P., Farssi, Y., Frénois, C., Levelut, A., Toulouse, J., Ziolkiewicz, S., J. Phys. I (France) 4 1217 (1994). The dielectric properties of K1−vLivTaO3 in the high temperature phase are well described by an power law distribution of relaxation time with x≈T/To>1.1.>Google Scholar
[17] Bardou, F., Bouchaud, J.P., Emile, O., Aspect, A., Cohen-Tannouji, C., Phys. Rev. Lett 72 203 (1994)Google Scholar