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A Universal Lower Bound for the Complexity of Gaussian-Divisible Spin Glasses
Abstract
We consider a variant of the spherical mixed spin glass model with non-Gaussian disorder. Specifically, we replace the usual standard Gaussian interaction coefficients with Gaussian-divisible ones, meaning that each coefficient can be expressed as the sum of a standard Gaussian random variable and an independent, non-Gaussian random variable. We show that the annealed complexity of this model is at least the annealed complexity of the standard Gaussian model, if the non-Gaussian part is centered and subexponential.
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BibTeX
@misc{kivimae2026universal,
title = {{A Universal Lower Bound for the Complexity of Gaussian-Divisible Spin Glasses}},
author = {Pax Kivimae and Benjamin McKenna},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23823},
eprint = {2610.23823},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23823},
}
RIS
TY - UNPB
TI - A Universal Lower Bound for the Complexity of Gaussian-Divisible Spin Glasses
AU - Pax Kivimae
AU - Benjamin McKenna
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23823
UR - https://arxiv.org/abs/2610.23823
AB - We consider a variant of the spherical mixed spin glass model with non-Gaussian disorder. Specifically, we replace the usual standard Gaussian interaction coefficients with Gaussian-divisible ones, meaning that each coefficient can be expressed as the sum of a standard Gaussian random variable and an independent, non-Gaussian random variable. We show that the annealed complexity of this model is at least the annealed complexity of the standard Gaussian model, if the non-Gaussian part is centered and subexponential.
ER -