{
  "abstract": "We study upper large deviations of the free energy of mixed $p$-spin Ising spin glasses through the generalized TAP free energy $F_{\\mathrm{TAP}}$ of Chen, Panchenko and Subag. For every mixture with radius of convergence greater than one, $\\max F_{\\mathrm{TAP}}$ 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 $\\sum_p 2^pβ_p^2<\\infty$, 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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06490",
  "author_total": 1,
  "authors": [
    {
      "name": "Yan Ru Pei"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/epbtkex154n0g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06490",
  "fulltext_url": null,
  "id": "epbtkex154n0g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06490",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.dis-nn"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "3104|Theoretical and Computational Physics"
    ]
  ],
  "openalex": "W7220695760",
  "pdf_url": "https://arxiv.org/pdf/2610.06490",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/epbtkex154n0g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:37Z",
      "native_id": "2610.06490",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06490"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    }
  ],
  "title": "TAP states at upper deviations of the free energy: existence, localization and marginal stability in Ising spin glasses",
  "title_text": "TAP states at upper deviations of the free energy: existence, localization and marginal stability in Ising spin glasses",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/epbtkex154n0g",
  "venue": "arXiv",
  "versions": []
}