TY - JOUR

T1 - Glauber dynamics of the random energy model

T2 - II. Aging below the critical temperature

AU - Ben Arous, Gérard

AU - Bovier, Anton

AU - Gayrard, Véronique

PY - 2003/5

Y1 - 2003/5

N2 - 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 auto-correlation 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.

AB - 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 auto-correlation 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.

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U2 - 10.1007/s00220-003-0799-3

DO - 10.1007/s00220-003-0799-3

M3 - Article

AN - SCOPUS:0038806647

SN - 0010-3616

VL - 236

SP - 1

EP - 54

JO - Communications In Mathematical Physics

JF - Communications In Mathematical Physics

IS - 1

ER -