标题： 关于多尺度平均场自旋玻璃的相图 显示英文标题

标题： On the phase diagram of the multiscale mean-field spin-glass

摘要： 在本文中，我们研究了施林顿-基尔帕特里克（SK）模型的相图，其中耦合被强制在不同的时间尺度上热化。 除了作为SK模型的一个具有挑战性的推广之外，这种设置可能在物理学中自然出现，当系统的一部分自由度比其他部分更快地弛豫到平衡时。 对于这个模型，我们计算了重叠分布的二阶矩的渐近值。 此外，我们提供了一个用于退火解成立的严格充分条件，确定了一个高温区域。 另外，我们还证明了在足够低的温度下，解必须表现出至少与多尺度模型中已有的时间尺度数量相等的复现对称性破缺层次。 最后，我们给出了功能序参数支持域中存在间隙的充分条件。 显示英文摘要

摘要： In this paper we study the phase diagram of a Sherrington-Kirkpatrick (SK) model where the couplings are forced to thermalize at different times scales. Besides being a challenging generalization of the SK model, such settings may arise naturally in physics whenever part of the many degrees of freedom of a system relaxes to equilibrium considerably faster than the others. For this model we compute the asymptotic value of the second moment of the overlap distribution. Furthermore, we provide a rigorous sufficient condition for an annealed solution to hold, identifying a high temperature region. In addition, we also prove that for sufficiently low temperature the solution must present a number of replica symmetry breaking levels at least equal to the number of time scales already present in the multiscale model. Finally, we give a sufficient condition for the existence of gaps in the support of the functional order parameters.