On the spectral gap of spherical spin glass dynamics
On the spectral gap of spherical spin glass dynamics
复制标题
球形自旋玻璃动力学的光谱间隙
DOI：
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发表时间：
2016
影响因子：
1.5
通讯作者：
Aukosh Jagannath
中科院分区：
文献类型：
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作者：
Reza Gheissari;Aukosh Jagannath
我们考虑了系统尺寸为N的球形p -自旋玻璃模型的朗之万动力学的平衡时间。我们证明了在足够高的温度下，log-Sobolev常数和谱隙在$N$中为1阶，而在足够低的温度下，谱隙在$N$中呈指数衰减。这证实了在光谱间隙水平上存在动态高温相和动态玻璃相。这些结果的关键是对Subag- Zeitouni和Subag的极限过程和限制自由能的理解。
We consider the time to equilibrium for the Langevin dynamics of the spherical $p$-spin glass model of system size $N$. We show that the log-Sobolev constant and spectral gap are order $1$ in $N$ at sufficiently high temperature whereas the spectral gap decays exponentially in $N$ at sufficiently low temperatures. These verify the existence of a dynamical high temperature phase and a dynamical glass phase at the level of the spectral gap. Key to these results are the understanding of the extremal process and restricted free energy of Subag--Zeitouni and Subag.
影响因子：
2.4
作者：
Ben Arous, Gerard;Bovier, Anton;Cerny, Jiri
通讯作者：
Cerny, Jiri