{
  "abstract": "We prove continuity of the phase transition for long-range Bernoulli percolation on $\\mathbb{Z}^{2}$ with connection probabilities that decay at least exponentially fast. This extends earlier work by Duminil-Copin, Sidoravicius, and Tassion on slabs. Our proof establishes a finite-size criterion that allows us to run a renormalisation argument. As a corollary, we obtain supercritical sharpness, in the sense that for every $β>β_c$, there exists a unique macroscopic cluster in large boxes with high probability.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35233",
  "author_total": 4,
  "authors": [
    {
      "name": "Omer Angel"
    },
    {
      "name": "Daniel de la Riva"
    },
    {
      "name": "Christoforos Panagiotis"
    },
    {
      "name": "Yuliang Shi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2b1xthtxq7fb4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35233",
  "fulltext_url": null,
  "id": "2b1xthtxq7fb4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35233",
  "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",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7223926703",
  "pdf_url": "https://arxiv.org/pdf/2610.35233",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2b1xthtxq7fb4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.35233",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35233"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Continuity of the phase transition for long-range Bernoulli percolation with exponential decay on $\\mathbb{Z}^{2}$",
  "title_text": "Continuity of the phase transition for long-range Bernoulli percolation with exponential decay on ℤ^2",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/2b1xthtxq7fb4",
  "venue": "arXiv",
  "versions": []
}