具有正交不变耦合的伊辛自旋玻璃的复制对称自由能

IF 1.5 1区 数学 Q2 STATISTICS & PROBABILITY
Zhou Fan, Yihong Wu
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引用次数: 0

摘要

我们研究了带有外部磁场的谢林顿-柯克帕特里克(S-K)自旋玻璃模型的一个变体,其中的随机对称耦合矩阵不包含 i.i.d. 项,而是具有正交不变性。对于足够高的温度,我们证明了模型自由能一阶极限的复制对称公式。我们的分析是对博尔索森之前为研究 S-K 模型的高温机制而引入的条件次动量法论证的改编,其中的一个条件是近似信息传递(AMP)算法的迭代,用于求解模型磁化的 TAP 方程。我们使用免记忆版本的 AMP 来应用这种方法,它是根据模型耦合的正交不变结构量身定制的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The replica-symmetric free energy for Ising spin glasses with orthogonally invariant couplings

We study a variant of the Sherrington–Kirkpatrick (S–K) spin glass model with external field, where the random symmetric couplings matrix does not consist of i.i.d. entries but is instead orthogonally invariant in law. For sufficiently high temperature, we prove a replica-symmetric formula for the first-order limit of the model free energy. Our analysis is an adaptation of a conditional second-moment-method argument previously introduced by Bolthausen for studying the high-temperature regime of the S–K model, where one conditions on the iterates of an Approximate Message Passing (AMP) algorithm for solving the TAP equations for the model magnetization. We apply this method using a memory-free version of AMP that is tailored to the orthogonally invariant structure of the model couplings.

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来源期刊
Probability Theory and Related Fields
Probability Theory and Related Fields 数学-统计学与概率论
CiteScore
3.70
自引率
5.00%
发文量
71
审稿时长
6-12 weeks
期刊介绍: Probability Theory and Related Fields publishes research papers in modern probability theory and its various fields of application. Thus, subjects of interest include: mathematical statistical physics, mathematical statistics, mathematical biology, theoretical computer science, and applications of probability theory to other areas of mathematics such as combinatorics, analysis, ergodic theory and geometry. Survey papers on emerging areas of importance may be considered for publication. The main languages of publication are English, French and German.
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