PreprintCC BY-SA 4.0arXiv
A formula for the free energy of non-convex vector spin glasses
Abstract
We consider vector mean-field spin glass models with independent and identically distributed spins without assuming the covariance function is convex. We identify the limit free energy as the minimum of a functional that can be written as the sum of a relative entropy and the solution of a Hamilton--Jacobi equation. The proof of this result relies on the observation that when the spin configurations of the system are constrained to have a given empirical measure, the corresponding free energy approximately satisfies a Hamilton--Jacobi equation with a uniformly bounded error.
Related
- Convergence of the free energy of vector spin glasses with non-convex interactions
- Free energy of non-convex multi-species spin glasses with centered Ising spins
- Free energy of non-convex multi-species spherical spin glasses
- Free energy of spherical vector spin glasses
- Free energy of non-convex multi-species Ising spin glasses with external fields
BibTeX
@misc{chen2026formula,
title = {{A formula for the free energy of non-convex vector spin glasses}},
author = {Hong-Bin Chen and Fu-Hsuan Ho and Victor Issa},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18744},
eprint = {2610.18744},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18744},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - A formula for the free energy of non-convex vector spin glasses
AU - Hong-Bin Chen
AU - Fu-Hsuan Ho
AU - Victor Issa
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18744
UR - https://arxiv.org/abs/2610.18744
AB - We consider vector mean-field spin glass models with independent and identically distributed spins without assuming the covariance function is convex. We identify the limit free energy as the minimum of a functional that can be written as the sum of a relative entropy and the solution of a Hamilton--Jacobi equation. The proof of this result relies on the observation that when the spin configurations of the system are constrained to have a given empirical measure, the corresponding free energy approximately satisfies a Hamilton--Jacobi equation with a uniformly bounded error.
ER -