{
  "abstract": "For $Δ\\ge2$ and $q\\ge11Δ/6$, we prove that the antiferromagnetic $q$-state Potts partition function on finite simple graphs of maximum degree at most $Δ$ has no Fisher zeros in a graph-uniform complex neighbourhood of $[0,1]$. For $q>11Δ/6$, the proof establishes coupling independence throughout $[0,1]$ using a soft version of Vigoda's flip dynamics. Our main tool is a separator-shell transfer theorem for the Potts model on induced-subgraph closed classes of graphs of maximum degree at most $Δ$, with $q\\geΔ+1$. It yields a graph-uniform zero-free neighbourhood of $[0,1]$ from Hamming coupling independence at $0$ and a uniform coupling-independence bound on each interval $[δ,1]$, $δ\\in(0,1]$. We also obtain zero-free Lee-Yang polydiscs around the uniform field for vertex- and edge-colour fields. For Boolean Holant problems on bounded-degree graphs whose signatures come from a fixed finite family of log-concave symmetric signatures $f$ with $f(0)>0$, such as $b$-matchings, we obtain graph-uniform zero-free polytubes around every bounded box of nonnegative activities; their union is an open zero-free neighbourhood of the nonnegative orthant. An appendix summarizes further coupling-independence inputs and the zero-free regions they yield.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12456",
  "author_total": 2,
  "authors": [
    {
      "name": "Shuai Shao"
    },
    {
      "name": "Ke Shi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0bvwnmw65hahh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12456",
  "fulltext_url": null,
  "id": "0bvwnmw65hahh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12456",
  "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",
      "cs.DS"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "3104|Theoretical and Computational Physics"
    ]
  ],
  "openalex": "W7221067472",
  "pdf_url": "https://arxiv.org/pdf/2610.12456",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0bvwnmw65hahh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:54Z",
      "native_id": "2610.12456",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12456"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Coupling Independence Implies Zero-Freeness",
  "title_text": "Coupling Independence Implies Zero-Freeness",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/0bvwnmw65hahh",
  "venue": "arXiv",
  "versions": []
}