{
  "abstract": "We derive the $\\mathcal{P}(Φ)_2$ measure on the two-dimensional unit torus as the rigorous limit of many-body quantum Gibbs states. In particular, the quantum model corresponding to the $Φ^{2p}_2$ measure is formulated in the grand-canonical ensemble with a general symmetric $p$-body interaction potential which is not required to have a factorized form. Unlike in the $Φ^4_2$ case investigated by Fröhlich--Knowles--Schlein--Sohinger in \\cite{FKSS25}, in the treatment of higher-order interactions, Wick renormalization generates a full hierarchy of lower-order interactions which we organize systematically using a graphical formalism. One key ingredient of our analysis is a logarithmic stability estimate for both the nonlocal Hartree functional and the many-body Hamiltonian that is uniform in the interaction range, allowing us to use the positivity of the leading $p$-body interaction to control all lower-order terms generated by the Wick counterterms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.23084",
  "author_total": 3,
  "authors": [
    {
      "name": "Phan Thành Nam"
    },
    {
      "name": "Zhilin Yang"
    },
    {
      "name": "Xiangchan Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8ssh735m9aqj2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.23084",
  "fulltext_url": null,
  "id": "8ssh735m9aqj2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.23084",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7171552866",
  "pdf_url": "https://arxiv.org/pdf/2607.23084",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8ssh735m9aqj2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:36Z",
      "native_id": "2607.23084",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.23084"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "$\\mathcal{P}(Φ)_2$ Theory from many-body quantum Gibbs states",
  "title_text": "𝒫(Φ)_2 Theory from many-body quantum Gibbs states",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/8ssh735m9aqj2",
  "venue": "arXiv",
  "versions": []
}