{
  "abstract": "The Lee-Yang circle theorem places every zero of a ferromagnetic Ising partition polynomial on the unit circle. The arc condition, that every zero lie in the closed left half-plane, turns the circle theorem into a product formula for the characteristic function of the occupation count and makes it usable for local limit theorems. For the two-row periodic Ising torus we give the exact reflection factorization of the row transfer matrix, reduce the crossing at zeta = i to a real cubic, and identify the critical coupling a_c* = 0.8637850566870... as the unique root in (0,1) of an explicit octic. We prove that every a > a_c* satisfies the arc condition simultaneously for all circumferences, that no smaller coupling does, and that the finite thresholds approach a_c* at the rate C/n^2 with an explicit algebraic constant C. The factorization and the 2x2 threshold are formalized in Lean 4 against Mathlib; the zeta = i reduction, uniformity and rate are analysis-level.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04165",
  "author_total": 1,
  "authors": [
    {
      "name": "Marco Mandap"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/621bwrydjmp48.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04165",
  "fulltext_url": null,
  "id": "621bwrydjmp48",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04165",
  "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",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04165",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/621bwrydjmp48.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04165",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04165"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "The Arc Threshold of the Two-Row Ising Torus: Exact Factorization, an Algebraic Critical Coupling, Uniformity in the Circumference, and the Rate of Convergence",
  "title_text": "The Arc Threshold of the Two-Row Ising Torus: Exact Factorization, an Algebraic Critical Coupling, Uniformity in the Circumference, and the Rate of Convergence",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/621bwrydjmp48",
  "venue": "arXiv",
  "versions": []
}