2021/05/06 by Zhou Fan, Yihong Wu, Fan, Zhou +1 · 1 citation
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Information Theory (cs.IT) #Probability (math.PR) #Random Matrices and Applications #Statistics Theory (math.ST) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2105.02797
openalex publication_date 2021/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.