{
  "abstract": "We consider the nearest-neighbour Ising model on $\\mathbb{Z}^d$, and establish sharp results for the normal approximation of the magnetisation throughout the high-temperature regime. In particular, we establish optimal Berry--Esseen bounds between the magnetisation in an arbitrary finite region and a Gaussian with the corresponding finite-volume variance. These results hold for finite-volume Gibbs measures with arbitrary boundary conditions, as well as for the infinite-volume Gibbs measure. We also determine sharp rates of convergence of the magnetisation in a finite box to a Gaussian with variance given by the infinite-volume susceptibility. For this fixed Gaussian target, we show that, in dimensions $d\\ge 3$, periodic boundary conditions yield strictly faster convergence than free boundary conditions. Our approach uses Stein's method to quantify the normal approximation error by analysing the semigroup of the continuous-time Ising heat-bath dynamics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25746",
  "author_total": 2,
  "authors": [
    {
      "name": "Timothy M. Garoni"
    },
    {
      "name": "Aram Perez"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8be5m4f4gpbbs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25746",
  "fulltext_url": null,
  "id": "8be5m4f4gpbbs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25746",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7223007228",
  "pdf_url": "https://arxiv.org/pdf/2610.25746",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8be5m4f4gpbbs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:52Z",
      "native_id": "2610.25746",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25746"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Berry--Esseen Bounds for High-Temperature Ising Models",
  "title_text": "Berry--Esseen Bounds for High-Temperature Ising Models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/8be5m4f4gpbbs",
  "venue": "arXiv",
  "versions": []
}