{
  "abstract": "Consider the Sachdev-Ye-Kitaev model with $N$ Majorana fermions and interaction order $q$. For even $4\\leq q\\ll \\sqrt{N}$, we present a microscopic framework that determines the free energy limit at every fixed inverse temperature $β>0$. In particular, this gives the first rigorous derivation of the Schwinger-Dyson thermodynamics of the model. For all even $q\\in \\{4,6,...,N-4\\}$, we further determine the asymptotic location of the largest eigenvalue, which answers a question posed by Feng-Tian-Wei \\cite{FengTianWei1}. Consequently, we obtained the free energy limit along every sequence $β\\equiv β_N\\to\\infty$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.18998",
  "author_total": 1,
  "authors": [
    {
      "name": "Yukun He"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1rj2sr7dn4kch.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.18998",
  "fulltext_url": null,
  "id": "1rj2sr7dn4kch",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.18998",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2613|Random Matrices and Applications"
    ]
  ],
  "openalex": "W7170080710",
  "pdf_url": "https://arxiv.org/pdf/2607.18998",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1rj2sr7dn4kch.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:22Z",
      "native_id": "2607.18998",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.18998"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Free energy and spectral edge of the SYK model",
  "title_text": "Free energy and spectral edge of the SYK model",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/1rj2sr7dn4kch",
  "venue": "arXiv",
  "versions": []
}