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arXiv · 2611.00747

Free energy of 2-spin spherical vector spin glasses

Hong-Bin Chen·Yanjin Xiang·Zhihua Zhang
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Abstract

We compute the limit of free energy of 2-spin spherical vector spin glasses with possibly non-convex interaction and couplings satisfying a finite fourth-moment assumption. The couplings need not be Gaussian. The limit is given by a logarithmic-determinant variational formula, equivalently by a finite-dimensional matrix Dyson equation, and its zero-temperature limit yields the ground-state energy. The limiting formulas depend only on the covariance of the couplings. We also study fluctuations: at an interior minimizer, an explicit variance bound transfers the limiting law of a logarithmic linear statistic to the free energy. For Gaussian couplings, this yields Gaussian fluctuations. At a boundary minimizer, assuming a simple regular edge with GOE Tracy-Widom fluctuations and a one-edge reduction, we transfer the edge fluctuations to the free energy.

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Hong-Bin Chen, Yanjin Xiang, Zhihua Zhang. 2026-10-31. Free energy of 2-spin spherical vector spin glasses. https://arxiv.org/abs/2611.00747

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