自旋玻璃中的碎裂与亚稳态
Shattering Versus Metastability in Spin Glasses
摘要：
我们在这项工作中的目标是更好地了解副本对称性破缺，粉碎和亚稳态之间的关系。为此，我们研究了静态和动态行为的球形纯$p$自旋玻璃以上的副本对称性破缺温度$T_{s}$。在这个制度中，我们发现，至少有两个不同的温度相关的非平凡的行为。首先，我们证明，有一个制度的温度，其中的球形$p$自旋模型表现出破碎相。我们的结果在高于但接近$T_s$的区域成立。然后，我们发现，亚稳态存在高达一个更高的温度$T_{BBM}$预测Barrat-Burioni-Mézard这是预计将高于相界的粉碎相$T_d <T_{BBM}$。我们开发这项工作，首先开发一个无边界的-安德森-帕尔默分解的基础上的工作Subag。然后，我们提出了一系列的问题，并就粉碎和缓慢混合的尖锐的相界。
英文摘要：
Our goal in this work is to better understand the relationship between replica symmetry breaking, shattering, and metastability. To this end, we study the static and dynamic behaviour of spherical pure $p$-spin glasses above the replica symmetry breaking temperature $T_{s}$. In this regime, we find that there are at least two distinct temperatures related to non-trivial behaviour. First we prove that there is a regime of temperatures in which the spherical $p$-spin model exhibits a shattering phase. Our results holds in a regime above but near $T_s$. We then find that metastable states exist up to an even higher temperature $T_{BBM}$ as predicted by Barrat--Burioni--Mézard which is expected to be higher than the phase boundary for the shattering phase $T_d <T_{BBM}$. We develop this work by first developing a Thouless--Anderson--Palmer decomposition which builds on the work of Subag. We then present a series of questions and conjectures regarding the sharp phase boundaries for shattering and slow mixing.
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