Mathematics > Probability
[Submitted on 6 May 2021 (v1), last revised 29 Sep 2021 (this version, v2)]
Title:The replica-symmetric free energy for Ising spin glasses with orthogonally invariant couplings
View PDFAbstract:We study the mean-field Ising spin glass model with external field, where the random symmetric couplings matrix is orthogonally invariant in law. For sufficiently high temperature, we prove that the replica-symmetric prediction is correct for the first-order limit of the free energy. Our analysis is an adaption of a "conditional quenched equals annealed" argument used by Bolthausen to analyze the high-temperature regime of the Sherrington-Kirkpatrick model. We condition on a sigma-field that is generated by the iterates of an Approximate Message Passing algorithm for solving the TAP equations in this model, whose rigorous state evolution was recently established.
Submission history
From: Zhou Fan [view email][v1] Thu, 6 May 2021 16:41:11 UTC (50 KB)
[v2] Wed, 29 Sep 2021 03:04:33 UTC (56 KB)
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