Free energy of 2-spin spherical vector spin glasses
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.
Related
- Free energy of spherical vector spin glasses
- Free energy of non-convex multi-species spherical spin glasses
- Convergence of the free energy of vector spin glasses with non-convex interactions
- A formula for the free energy of non-convex vector spin glasses
- Free energy of non-convex multi-species spin glasses with centered Ising spins
BibTeX
@misc{chen2026free,
title = {{Free energy of 2-spin spherical vector spin glasses}},
author = {Hong-Bin Chen and Yanjin Xiang and Zhihua Zhang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00747},
eprint = {2611.00747},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00747},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Free energy of 2-spin spherical vector spin glasses
AU - Hong-Bin Chen
AU - Yanjin Xiang
AU - Zhihua Zhang
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00747
UR - https://arxiv.org/abs/2611.00747
AB - 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.
ER -