论文标题
种植的XY模型：热力学和推理
The planted XY model: thermodynamics and inference
论文作者
论文摘要
在本文中，我们研究了一个完全连接的种植的自旋玻璃，名为“种植的XY”模型。研究该系统的动机既来自自旋玻璃场，又是统计推断之一，它模拟了角度同步问题。我们使用近似消息传递（AMP）算法及其状态进化（SE），在温度，铁磁偏置平面中得出复制品对称（RS）相图。虽然RS预测在Nishimori线上是精确的（即，当温度与铁磁偏置匹配时），但是当参数不匹配时，它们变得不准确，从而导致旋转玻璃相无法收敛的自旋玻璃相。为了克服RS近似值的缺陷，我们基于近似调查传播（ASP）算法进行了一步复制对称性破坏（1RSB）分析。利用ASP的状态演变，我们计算了该度量中亚稳态状态的数量，得出1RSB的自由熵，并在整个自旋玻璃相中找到巴黎参数的行为。
In this paper we study a fully connected planted spin glass named the planted XY model. Motivation for studying this system comes both from the spin glass field and the one of statistical inference where it models the angular synchronization problem. We derive the replica symmetric (RS) phase diagram in the temperature, ferromagnetic bias plane using the approximate message passing (AMP) algorithm and its state evolution (SE). While the RS predictions are exact on the Nishimori line (i.e. when the temperature is matched to the ferromagnetic bias), they become inaccurate when the parameters are mismatched, giving rise to a spin glass phase where AMP is not able to converge. To overcome the defects of the RS approximation we carry out a one-step replica symmetry breaking (1RSB) analysis based on the approximate survey propagation (ASP) algorithm. Exploiting the state evolution of ASP, we count the number of metastable states in the measure, derive the 1RSB free entropy and find the behavior of the Parisi parameter throughout the spin glass phase.
