Some properties of the phase diagram for mixed p-spin glasses
Some properties of the phase diagram for mixed p-spin glasses
复制标题
混合 p-自旋玻璃相图的一些性质
DOI：
10.1007/s00440-015-0691-z
复制
发表时间：
2015
影响因子：
2
通讯作者：
Ian Tobasco
中科院分区：
文献类型：
--
作者：
Aukosh Jagannath;Ian Tobasco
本文研究了具有伊辛自旋的混合p自旋玻璃的Parisi变分问题。我们的出发点是Parisi措施的起源在于在一阶最优性条件的Parisi功能，这是已知的严格凸的一个特征。利用这一特性，我们研究了温度-外场平面上的相图。我们开始推导自洽条件Parisi措施，推广那些德阿尔梅达和无尾对称破缺（RSB）和所有模型的所有级别。因此，我们推测，对于所有的模型的对称相位是由自然模拟的德阿尔梅达无边界条件所确定的区域。我们发现，对于所有的模型，该区域的互补是在RSB阶段。此外，我们还证明了固定相边界是平面上的相边界减去一个有界集。在Sherrington-Kirkpatrick模型的情况下，我们扩展了最后一个结果，表明这个有界集不包含零外场的临界点。
In this paper we study the Parisi variational problem for mixed p-spin glasses with Ising spins. Our starting point is a characterization of Parisi measures whose origin lies in the first order optimality conditions for the Parisi functional, which is known to be strictly convex. Using this characterization, we study the phase diagram in the temperature-external field plane. We begin by deriving self-consistency conditions for Parisi measures that generalize those of de Almeida and Thouless to all levels of Replica Symmetry Breaking (RSB) and all models. As a consequence, we conjecture that for all models the Replica Symmetric phase is the region determined by the natural analogue of the de Almeida–Thouless condition. We show that for all models, the complement of this region is in the RSB phase. Furthermore, we show that the conjectured phase boundary is exactly the phase boundary in the plane less a bounded set. In the case of the Sherrington–Kirkpatrick model, we extend this last result to show that this bounded set does not contain the critical point at zero external field.