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 -