{
  "abstract": "We give the first polynomial-time algorithm to estimate the partition function of the antiferromagnetic Ising model on the uniformly random $d$-regular graph to arbitrarily high accuracy for all inverse temperatures up to the Kesten-Stigum threshold. This is the entire regime in which the model is \"replica symmetric,\" and is conjectured to be optimal for polynomial-time counting and sampling. To achieve our algorithmic result, we establish the absence of Fisher zeros for the partition function in a constant-width strip around the interval from $0$ up to the Kesten-Stigum threshold, with high probability over the randomness of the input graph. AI Disclosure: The overarching vision and proof architecture were developed solely by the authors without AI input. GPT 5.5 Pro was used, with extensive guidance from the authors, for only a few minor technical aspects of the proof. The authors independently verified correctness and wrote everything by hand. We take full responsibility for its contents. A more detailed statement can be found in Section 1.2.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40598",
  "author_total": 5,
  "authors": [
    {
      "name": "Ferenc Bencs"
    },
    {
      "name": "Brice Huang"
    },
    {
      "name": "Daniel Z. Lee"
    },
    {
      "name": "Kuikui Liu"
    },
    {
      "name": "Guus Regts"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3fkc5hj9jbrjw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40598",
  "fulltext_url": null,
  "id": "3fkc5hj9jbrjw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40598",
  "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",
      "cond-mat.dis-nn"
    ],
    [
      "arxiv",
      "cs.DS"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ]
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  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40598",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3fkc5hj9jbrjw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:28Z",
      "native_id": "2610.40598",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40598"
    }
  ],
  "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": "On Zeros and Algorithms for Disordered Systems II: The Antiferromagnetic Ising Model up to Kesten-Stigum",
  "title_text": "On Zeros and Algorithms for Disordered Systems II: The Antiferromagnetic Ising Model up to Kesten-Stigum",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:53Z",
  "url": "https://research.draconitic.com/paper/3fkc5hj9jbrjw",
  "venue": "arXiv",
  "versions": []
}