The replica-symmetric free energy for Ising spin glasses with orthogonally invariant couplings
arXiv:2105.02797
Abstract
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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- Gardner formula for Ising perceptron models at small densities
- Local convexity of the TAP free energy and AMP convergence for Z2-synchronization
- Free Energy Subadditivity for Symmetric Random Hamiltonians