2022
DOI: 10.48550/arxiv.2201.09918
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Free energy of a diluted spin glass model with quadratic Hamiltonian

Abstract: We study a diluted mean-field spin glass model with a quadratic Hamiltonian. Our main result establishes the limiting free energy in terms of an integral of a family of random variables that are the weak limits of the quenched variances of the spins in the system with varying edge connectivity. The key ingredient in our argument is played by the identification of these random variables as the unique solution to a recursive distributional equation. Our results in particular provide the first example of the dilu… Show more

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