{
  "abstract": "The complex-temperature phase structure of the two-dimensional Potts model has remained largely unresolved despite decades of study. Here we determine the complex-temperature phase diagram of the 3-state Potts model, and uncover three gapless phases beyond the familiar ferromagnetic and paramagnetic phases. This is done by combining tensor-network free energies with the Poisson equation to compute the Fisher zero density in the thermodynamic limit. The resulting zero distribution unifies and revises long-standing conjectures on the zero loci, and outlines each phase. One is a non-conformal gapless phase, with an exponentially growing number of low-lying transfer-matrix levels distributed across all momentum sectors. The other two are Luttinger-liquid phases with complex-valued Luttinger parameters related by the Kramers-Wannier duality. At the antiferromagnetic critical point, the Luttinger parameter equals 3, while its limit from the adjacent Luttinger-liquid phase is 6. These findings reveal rich phase structures and unconventional critical behavior in a classical textbook model.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01771",
  "author_total": 3,
  "authors": [
    {
      "name": "Fang-Cheng Wang"
    },
    {
      "name": "Qi-Jun Ye"
    },
    {
      "name": "Xin-Zheng Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/86hrz16m2zvxk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01771",
  "fulltext_url": null,
  "id": "86hrz16m2zvxk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01771",
  "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",
      "cond-mat.stat-mech"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01771",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/86hrz16m2zvxk.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:59Z",
      "native_id": "2611.01771",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01771"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Three New Phases in the Two-Dimensional Potts Model at Complex Temperature",
  "title_text": "Three New Phases in the Two-Dimensional Potts Model at Complex Temperature",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:18Z",
  "url": "https://research.draconitic.com/paper/86hrz16m2zvxk",
  "venue": "arXiv",
  "versions": []
}