We study the Gibbs measure of mixed spherical $p$-spin glass models at low temperature, in (part of) the 1-RSB regime, including, in particular, models close to pure in an appropriate sense. We show that the Gibbs measure concentrates on spherical bands around deep critical points of the (extended) Hamiltonian restricted to the sphere of radius $\sqrt N q_\star$, where $q_\star^2$ is the rightmost point in the support of the overlap distribution. We also show that the relevant critical points are pairwise orthogonal for two different low temperatures. This allows us to explain why temperature chaos occurs for those models, in contrast to the pure spherical models.

中文翻译：

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低温下混合球面自旋玻璃中的几何和温度混沌：微扰机制

我们研究了混合球形 $p$-spin 玻璃模型在低温下的 Gibbs 测量，在（部分）1-RSB 制度中，特别包括在适当意义上接近纯的模型。我们表明，吉布斯测量集中在（扩展的）哈密顿量的深临界点周围的球带上，该临界点限于半径为 $\sqrt N q_\star$ 的球体，其中 $q_\star^2$ 是支持中最右边的点重叠分布。我们还表明，对于两个不同的低温，相关临界点是成对正交的。这使我们能够解释为什么这些模型与纯球形模型相比会发生温度混乱。