J. Phys. I France
Volume 7, Numéro 5, May 1997
Page(s) 691 - 710
DOI: 10.1051/jp1:1997185
J. Phys. I France 7 (1997) 691-710

Glauber Dynamics and Ageing

R. Mélin and P. Butaud

CRTBT-CNRS, 25 avenue des Martyrs, BP 166X, 38042 Grenoble Cedex, France

(Received 26 September 1996, received in final form 27 December 1996, accepted 14 January 1997)

The Glauber dynamics of various models (REM-like trap models, Brownian motion, BM model, Ising chain and SK model) is analyzed in relation with the existence of ageing. From a finite size Glauber matrix, we calculate a time $\tau_{\rm w}(N)$ after which the system has relaxed to the equilibrium state. The case of metastability is also discussed. If the only non zero overlaps between pure states are only self-overlaps (REM-like trap models, BM model), the existence or absence of ageing depends only on the behavior of the density of eigenvalues for small eigenvalues. We have carried out a detailed numerical and analytical analysis of the density of eigenvalues of the REM-like trap models. In this case, we show that the behavior of the density of eigenvalues for typical trap realizations is related to the spectral dimension of the equivalent random walk model.

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