Universality of the REM for dynamics of mean-field spin glasses
Universality of the REM for dynamics of mean-field spin glasses
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DOI：
10.1007/s00220-008-0565-7
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发表时间：
2008-09-01
影响因子：
2.4
通讯作者：
Cerny, Jiri
中科院分区：
文献类型：
--
作者：
Ben Arous, Gerard;Bovier, Anton;Cerny, Jiri
我们考虑了一种自旋玻璃的p-自旋Sherrington-柯克帕特里克模型的Glauber动力学，它可以看作是N维超立方体上简单随机游动的时间变化。我们证明了，对于所有p >= 3和所有逆温度β> 0，存在一个常数gamma（beta，p）> 0，使得对于所有指数时间尺度exp（gamma N），其中gamma < gamma（beta，p），适当重新标度的时钟过程（时变过程）收敛到一个alpha稳定从属子，其中alpha = gamma/beta（2）< 1。此外，在这些时间尺度上的动态表现出老化与时间相关函数收敛到这个α稳定从属反正弦定律。换句话说，直到重新标度，在这些时间尺度上（比系统的平衡时间短），p-自旋模型的动力学以与REM相同的方式老化，并通过扩展Bouchaud的类REM陷阱模型，证实后者是广泛系统的普遍老化机制。SK模型（p = 2的情况）似乎属于不同的普适类。
We consider a version of Glauber dynamics for a p-spin Sherrington- Kirkpatrick model of a spin glass that can be seen as a time change of simple random walk on the N-dimensional hypercube. We show that, for all p >= 3 and all inverse temperatures beta > 0, there exists a constant gamma (beta ,p) > 0, such that for all exponential time scales, exp(gamma N), with gamma < gamma(beta ,p), the properly rescaled clock process (time-change process) converges to an alpha-stable subordinator where alpha = gamma/beta(2) < 1. Moreover, the dynamics exhibits aging at these time scales with a time-time correlation function converging to the arcsine law of this alpha-stable subordinator. In other words, up to rescaling, on these time scales (that are shorter than the equilibration time of the system) the dynamics of p-spin models ages in the same way as the REM, and by extension Bouchaud's REM-like trap model, confirming the latter as a universal aging mechanism for a wide range of systems. The SK model (the case p = 2) seems to belong to a different universality class.