Communications in Mathematical Physics Glauber Dynamics of the Random Energy Model II . Aging Below the Critical Temperature ∗
Communications in Mathematical Physics Glauber Dynamics of the Random Energy Model II . Aging Below the Critical Temperature ∗
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数学物理通讯随机能量模型的格劳伯动力学 II 。
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
V. Gayrard
中科院分区：
文献类型：
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作者：
G. B. Arous;Anton Bovier;V. Gayrard
我们研究了在临界温度以下随机能量模型的Glauber动力学的长期行为。我们建立了一个适当选择的时间尺度，发散与系统的大小，可以证明一个自然的自相关函数表现出老化。此外，我们还证明了该函数的长期渐近性与Bouchaud和Dean提出的所谓“类rem陷阱模型”的渐近性一致。我们的结果依赖于对极低能量的不同状态之间的过程的过渡时间分布的非常精确的估计。
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.