论文标题
在高温下正交旋转眼镜的龙头方程式
TAP equations for orthogonally invariant spin glasses at high temperature
论文作者
论文摘要
我们研究了平均场自旋玻璃模型的高温状态，该模型的耦合矩阵在法律上是正交的。该模型的磁化是为了满足TAP方程系统的磁性化，该系统最初是使用Gibbs自由能的图表膨胀来得出的。我们证明，在足够高温的制度下，在$ l^2 $的情况下，此点击描述是正确的。我们的方法开发了一种新颖的几何论点，用于证明传递近似消息传递（AMP）算法的收敛性，该算法适用于没有I.I.D.的模型。耦合。通过在AMP算法的输出周围的薄带的自由能的有条件的第二矩分析中，在许多“正交”复制品的系统中显示了这种收敛性。
We study the high-temperature regime of a mean-field spin glass model whose couplings matrix is orthogonally invariant in law. The magnetization of this model is conjectured to satisfy a system of TAP equations, originally derived by Parisi and Potters using a diagrammatic expansion of the Gibbs free energy. We prove that this TAP description is correct in an $L^2$ sense, in a regime of sufficiently high temperature. Our approach develops a novel geometric argument for proving the convergence of an Approximate Message Passing (AMP) algorithm to the magnetization vector, which is applicable in models without i.i.d. couplings. This convergence is shown via a conditional second moment analysis of the free energy restricted to a thin band around the output of the AMP algorithm, in a system of many "orthogonal" replicas.
