{
  "abstract": "We study the full-plane two-state fuzzy $4$-Potts model, obtained by assigning independent balanced $\\{\\pm1\\}$ spins to the open clusters of a critical $q=4$ random-cluster configuration. Its spin field has the same law as a single-spin projection and as the polarization field of the isotropic Ashkin--Teller model at its Potts point. We prove that, after proper normalization, all even multi-point spin correlation functions converge to explicit conformally covariant Coulomb-gas type neutral charge sums. As a consequence, we prove convergence in law of the rescaled magnetization field and identify its limit in law with $2\\mathopen{:}\\cos(X/2)\\mathclose{:}$ for a full-plane Gaussian free field $X$. The proof combines the Baxter--Kelland--Wu coupling, convergence of the six-vertex height function to the Gaussian free field, and a charge-completion mechanism: an enlarged discrete sum over charge assignments with total charge in $4\\mathbb Z$ produces a combinatorial cancellation of connection patterns, while only the neutral charge sector survives in the scaling limit.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.31374",
  "author_total": 2,
  "authors": [
    {
      "name": "Hong-Bin Chen"
    },
    {
      "name": "Jiaming Xia"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4gc95xaxtjc4t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.31374",
  "fulltext_url": null,
  "id": "4gc95xaxtjc4t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.31374",
  "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.stat-mech"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7163043450",
  "pdf_url": "https://arxiv.org/pdf/2605.31374",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4gc95xaxtjc4t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2605.31374",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.31374"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Multi-point functions of a full-plane two-state fuzzy $4$-Potts model",
  "title_text": "Multi-point functions of a full-plane two-state fuzzy $4$-Potts model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/4gc95xaxtjc4t",
  "venue": "arXiv",
  "versions": []
}