TAP states at upper deviations of the free energy: existence, localization and marginal stability in Ising spin glasses
Abstract
We study upper large deviations of the free energy of mixed p-spin Ising spin glasses through the generalized TAP free energy FTAP of Chen, Panchenko and Subag. For every mixture with radius of convergence greater than one, max FTAP and log ZN have the same large deviations at speed N; the proof combines their band theorem with Ramsey's theorem. For convex mixtures with ∑p 2pβp2<∞, upper deviations at level f are carried by generalized TAP critical points, which exist at the free-energy rate without Boursier's strict Plefka condition. Outside an event of smaller exponential order, near-maximizers at level f lie near the contact set of a constrained Parisi obstacle, follow the Auffinger-Chen field law, and have Hessian bulk near a reflected Pastur law whose edge is nonpositive and vanishes exactly at contacts where the obstacle is flat to second order. Where every contact is of this kind, a fixed stability margin costs rate.
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BibTeX
@misc{pei2026states,
title = {{TAP states at upper deviations of the free energy: existence, localization and marginal stability in Ising spin glasses}},
author = {Yan Ru Pei},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06490},
eprint = {2610.06490},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06490},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - TAP states at upper deviations of the free energy: existence, localization and marginal stability in Ising spin glasses
AU - Yan Ru Pei
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.06490
UR - https://arxiv.org/abs/2610.06490
AB - We study upper large deviations of the free energy of mixed p-spin Ising spin glasses through the generalized TAP free energy F_TAP of Chen, Panchenko and Subag. For every mixture with radius of convergence greater than one, max F_TAP and log Z_N have the same large deviations at speed N; the proof combines their band theorem with Ramsey's theorem. For convex mixtures with ∑_p 2^pβ_p^2<∞, upper deviations at level f are carried by generalized TAP critical points, which exist at the free-energy rate without Boursier's strict Plefka condition. Outside an event of smaller exponential order, near-maximizers at level f lie near the contact set of a constrained Parisi obstacle, follow the Auffinger-Chen field law, and have Hessian bulk near a reflected Pastur law whose edge is nonpositive and vanishes exactly at contacts where the obstacle is flat to second order. Where every contact is of this kind, a fixed stability margin costs rate.
ER -