PreprintCC BY 4.0arXiv
Universality of Annealed Complexity in the Spherical Pure p-Spin Model
Abstract
In an influential work, Auffinger, Ben Arous, and Černý (2013) investigated the limiting annealed complexity in the spherical pure p-spin model associated to the Gaussian disorder. Their results, in particular, included an explicit expression for the total number of critical points of the Hamiltonian below any given energy level. In this paper, we consider the same anneal complexity associated to a disorder interpolating between an arbitrary random variable and its Gaussian counterpart. Assuming strict subgaussianity of the former, our result shows that the annealed complexity shares the same limit as in the Gaussian case.
Related
- Spin Toda systems and N-point spherical Whittaker functions
- Free energy of non-convex multi-species spherical spin glasses
- Free energy of spherical vector spin glasses
- Free energy of 2-spin spherical vector spin glasses
- Approximating the Gibbs Measure of Spherical Spin Glasses to Within o(N−1/2) in the Replica Symmetric Phase
BibTeX
@misc{chen2026universality,
title = {{Universality of Annealed Complexity in the Spherical Pure $p$-Spin Model}},
author = {Wei-Kuo Chen and Te-Lun Lu and Arnab Sen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23701},
eprint = {2610.23701},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23701},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Universality of Annealed Complexity in the Spherical Pure p-Spin Model
AU - Wei-Kuo Chen
AU - Te-Lun Lu
AU - Arnab Sen
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23701
UR - https://arxiv.org/abs/2610.23701
AB - In an influential work, Auffinger, Ben Arous, and Černý (2013) investigated the limiting annealed complexity in the spherical pure p-spin model associated to the Gaussian disorder. Their results, in particular, included an explicit expression for the total number of critical points of the Hamiltonian below any given energy level. In this paper, we consider the same anneal complexity associated to a disorder interpolating between an arbitrary random variable and its Gaussian counterpart. Assuming strict subgaussianity of the former, our result shows that the annealed complexity shares the same limit as in the Gaussian case.
ER -