The multi-species mean-field spin-glass on the Nishimori line

Abstract

In this paper we study a multi-species disordered model on the Nishimori line. The typical properties of this line, a set of identities and inequalities among correlation functions, allow us to prove the replica symmetry i.e. the concentration of the order parameter. When the interaction structure is elliptic we rigorously compute the exact solution of the model in terms of a finite dimensional variational principle and we study its properties.

arXiv comment26 pages, one figure, to appear in Journal of Statistical Physics

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• Statistical limits of dictionary learning: random matrix theory and the spectral replica method
• Free energy in multi-species mixed $p$-spin spherical models
• An inference problem in a mismatched setting: a spin-glass model with Mattis interaction
• Fluctuation results for Multi-species Sherrington-Kirkpatrick model in the replica symmetric regime
• Hopfield model with planted patterns: a teacher-student self-supervised learning model
• Estimating rank-one matrices with mismatched prior and noise: universality and large deviations
• Strong replica symmetry for high-dimensional disordered log-concave Gibbs measures
• Anomalous distribution of magnetization in an Ising spin glass with correlated disorder
• Gibbs-Bogoliubov inequality on Nishimori line
• Analyticity of the energy in an Ising spin glass with correlated disorder
• Gauge theory for mixed $p$-spin glasses
• Toward mean-field bound for critical temperature on Nishimori line