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Aging in the random energy model

G. Ben Arous·A. Bovier·V. Gayrard
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Abstract

In this letter we announce rigorous results on the phenomenon of aging in the Glauber dynamics of the random energy model and their relation to Bouchaud's 'REM-like' trap model. We show that, below the critical temperature, if we consider a time-scale that diverges with the system size in such a way that equilibrium is almost, but not quite reached on that scale, a suitably defined autocorrelation function has the same asymptotic behaviour than its analog in the trap model.

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G. Ben Arous, A. Bovier, V. Gayrard. 2001-10-11. Aging in the random energy model. https://doi.org/10.1103/physrevlett.88.087201

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