{
  "abstract": "We study the cubic mean field Ising model with three body and two body interactions and an external field. Our main result is a complete classification of the global maximizers of the variational pressure in the full three-parameter region $(K,J,h)\\in(0,\\infty)\\times\\mathbb R^2$. We identify a coexistence surface with two nondegenerate global maximizers and a critical curve with a unique quartically degenerate maximizer; elsewhere the maximizer is unique and nondegenerate. This extends the phase diagrams previously obtained on two-parameter subfamilies \\cite{CMO24,O24}. As applications of the general results in \\cite{CR}, we give explicit magnetization fluctuation theorems and asymptotic distributions for one-parameter maximum likelihood estimators in the resulting regimes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25653",
  "author_total": 2,
  "authors": [
    {
      "name": "Van Hao Can"
    },
    {
      "name": "Viet Tinh Dang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/56x0tpaasd0t2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25653",
  "fulltext_url": null,
  "id": "56x0tpaasd0t2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25653",
  "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",
      "math.PR"
    ],
    [
      "openalex",
      "3104|Theoretical and Computational Physics"
    ]
  ],
  "openalex": "W7223033402",
  "pdf_url": "https://arxiv.org/pdf/2610.25653",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/56x0tpaasd0t2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25653",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25653"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Phase diagram and fluctuations in the cubic mean field Ising model",
  "title_text": "Phase diagram and fluctuations in the cubic mean field Ising model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/56x0tpaasd0t2",
  "venue": "arXiv",
  "versions": []
}