标题： 关于无序系统零点和算法：平均场自旋玻璃 显示英文标题

标题： On zeros and algorithms for disordered systems: mean-field spin glasses

摘要： 自旋玻璃是统计物理、平均情况计算复杂性理论和现代高维统计推断核心的基本概率分布。 在平均场设置中，我们设计了确定性的准多项式时间算法，用于在第二矩区域中的几乎所有逆温度下以任意高精度估计分区函数。 特别是，对于谢林顿-基尔帕特里克模型，我们的算法在几乎整个对称副本相位中都能成功。 为了实现这一点，我们研究了分区函数零点的位置。 值得注意的是，我们的方法在概念上很简单，并且同样适用于球面情况和伊辛自旋的情况。 显示英文摘要

摘要： Spin glasses are fundamental probability distributions at the core of statistical physics, the theory of average-case computational complexity, and modern high-dimensional statistical inference. In the mean-field setting, we design deterministic quasipolynomial-time algorithms for estimating the partition function to arbitrarily high accuracy for nearly all inverse temperatures in the second moment regime. In particular, for the Sherrington--Kirkpatrick model, our algorithms succeed for almost the entire replica-symmetric phase. To achieve this, we study the locations of the zeros of the partition function. Notably, our methods are conceptually simple, and apply equally well to the spherical case and the case of Ising spins.