Communications in Mathematical Physics

, Volume 236, Issue 1, pp 1–54

Glauber Dynamics of the Random Energy Model

II. Aging Below the Critical Temperature

Authors

  • Gérard Ben Arous
    • Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland. E-mail: benarous@cims.nyu.edu
  • Anton Bovier
    • Weierstrass-Institut für Angewandte Analysis und Stochastik, Mohrenstrasse 39, 10117 Berlin, Germany. E-mail: bovier@wias-berlin.de
  • Véronique Gayrard
    • Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland. E-mail: benarous@cims.nyu.edu

DOI: 10.1007/s00220-003-0799-3

Cite this article as:
Arous, G., Bovier, A. & Gayrard, V. Commun. Math. Phys. (2003) 236: 1. doi:10.1007/s00220-003-0799-3

Abstract:

 We investigate the long-time behavior of the Glauber dynamics for the random energy model below the critical temperature. We establish that for a suitably chosen timescale that diverges with the size of the system, one can prove that a natural autocorrelation function exhibits aging. Moreover, we show that the long-time asymptotics of this function coincide with those of the so-called ``REM-like trap model'' proposed by Bouchaud and Dean. Our results rely on very precise estimates on the distribution of transition times of the process between different states of extremely low energy.

Copyright information

© Springer-Verlag Berlin Heidelberg 2003