{
  "abstract": "We study the root-of-unity limit of the multi-component spin solution of the star-star relation whose Boltzmann weights are products of lens elliptic gamma functions, and whose spins take values in $\\mathbb{R}^{n-1}\\times(\\mathbb{Z}_r)^{n-1}$. When one of the elliptic nomes tends to a primitive $2rN$-th root of unity, the quasi-classical expansion gives at leading order the classical star-star relation of the Bazhanov-Sergeev multi-spin model; at the next order, under the standard assumptions on the saddle points, a $(\\mathbb{Z}_{rN})^{n-1}$-state solution of the star-star relation, which depends on $r$ and $N$ only through $rN$. Real $\\mathbb{Z}_n$-symmetric configurations of the continuous spins give elliptic $\\mathfrak{sl}(n)$ Kashiwara-Miwa type models labeled by $n$-torsion points. Extended to general primitive torsion points, these include the broken $\\mathbb{Z}_{rN}$ model of Quano and Fujii, for which the star-star relation follows from their Yang-Baxter equation when $\\gcd(n,rN)=1$. In the trigonometric limit the saddle point equations single out the spectral curve of the $\\mathfrak{sl}(n)$ chiral Potts model of Bazhanov, Kashaev, Mangazeev and Stroganov, and the Boltzmann weights become those of that model.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41438",
  "author_total": 1,
  "authors": [
    {
      "name": "Masahito Yamazaki"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0rf51pk0bvedp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41438",
  "fulltext_url": null,
  "id": "0rf51pk0bvedp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41438",
  "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",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "nlin.SI"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41438",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0rf51pk0bvedp.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:15Z",
      "native_id": "2610.41438",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41438"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Root-of-unity limit of the $A_{n-1}$ lens elliptic gamma function solution of the star-star relation",
  "title_text": "Root-of-unity limit of the A_n−1 lens elliptic gamma function solution of the star-star relation",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/0rf51pk0bvedp",
  "venue": "arXiv",
  "versions": []
}