{
  "abstract": "We study the von Neumann algebra generated by a quasi-product state associated with the one-dimensional hard-core lattice gas. If \\(κ>0\\) denotes the activity (fugacity), the transfer-matrix construction gives the stationary transition matrix \\[ P=\\begin{pmatrix}p&q\\\\ 1&0\\end{pmatrix}, \\qquad p+q=1, \\qquad κ=\\frac{q}{p^2}. \\] The stationary Markov measure on the hard-core path space induces a faithful diagonal state on the corresponding path \\(AF\\)-algebra. We give a state-preserving identification of its GNS von Neumann algebra with the Feldman--Moore algebra of the measured tail equivalence relation. The relation is hyperfinite and ergodic, and its nonzero ratio set is \\(κ^{\\mathbb Z}\\). Consequently, the generated algebra is the hyperfinite factor of type \\(\\mathrm{II}_1\\) when \\(κ=1\\), and of type \\(\\mathrm{III}_λ\\), where \\(λ=\\min\\{κ,κ^{-1}\\}\\), when \\(κ\\ne1\\). The point \\(κ=1\\) is not a thermodynamic phase transition: the pressure and particle density are analytic for all \\(κ>0\\). We also describe the precise support-corner relation with the GNS algebra of the diagonal Gibbs state on the quasi-local spin algebra, and we determine the centralizer and the flow of weights.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.12458",
  "author_total": 2,
  "authors": [
    {
      "name": "Farrukh Mukhamedov"
    },
    {
      "name": "Yuri Suhov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/07a6h58v1sb3c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.12458",
  "fulltext_url": null,
  "id": "07a6h58v1sb3c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.12458",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.OA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2606.12458",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/07a6h58v1sb3c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2606.12458",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.12458"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Quasi-Product States and Factor Types for the One-Dimensional Hard-Core Model",
  "title_text": "Quasi-Product States and Factor Types for the One-Dimensional Hard-Core Model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/07a6h58v1sb3c",
  "venue": "arXiv",
  "versions": []
}