Approximating the Gibbs Measure of Spherical Spin Glasses to Within o(N^−1/2) in the Replica Symmetric Phase

@misc{huang2026approximating,
  title = {{Approximating the Gibbs Measure of Spherical Spin Glasses to Within $o(N^-1/2)$ in the Replica Symmetric Phase}},
  author = {Brice Huang and Andrea Montanari and Huy Tuan Pham},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.32649},
  eprint = {2610.32649},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.32649},
}

TY  - UNPB
TI  - Approximating the Gibbs Measure of Spherical Spin Glasses to Within o(N^−1/2) in the Replica Symmetric Phase
AU  - Brice Huang
AU  - Andrea Montanari
AU  - Huy Tuan Pham
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.32649
UR  - https://arxiv.org/abs/2610.32649
AB  - We study the magnetization vector of mixed spherical spin glasses in a weak external field, in the replica symmetric phase. We derive a coordinatewise expansion of the magnetization which includes the leading cubic correction to the quadratic approximation, with an error that is o(N^−1/2) per coordinate. We also prove a corresponding high-moment bound for the full vector. Finally, our companion paper applies these estimates to the effective Hamiltonian obtained by restricting a tilted spherical spin glass to a narrow band around a TAP critical point. The resulting sharp approximation is designed for applications in which normalized Wasserstein accuracy is insufficient, including total-variation sampling by stochastic localization.
ER  -