{
  "abstract": "We study the ferromagnetic Ising model on finite hyperbolic tessellations of Euclidean AdS$_2$ with open and wired boundary conditions. Because a finite fraction of spins remains at the boundary as the lattice grows, these conditions select distinct thermodynamic behaviours. In the $\\{5,4\\}$ tessellation, Monte-Carlo simulations using efficient worm algorithms on open boundaries (OBC) yield a transition near $β_c J=0.632(3)$, with susceptibility data collapsing under scaling by the total number of spins $N$. The fitted finite-size exponents, $1/\\barν \\simeq 0.162$ and $γ/\\barν \\simeq 0.743$, differ substantially from the mean-field volume scaling. Wired boundaries (WBC), which correlate boundary spins, instead show a transition around $β_c J=0.348(4)$ to an ordered phase consistent with the mean-field exponents. While the mean-field criticality with WBC is consistent with previous studies and with the suppression of independent boundary fluctuations, the OBC exponents hint at the presence of a new universality class. Results from other tessellations support the robustness of the observed scaling with OBC. We discuss a possible route to interpolate between the different boundary conditions. Our findings show that boundary dynamics must be specified when characterizing critical behaviour on hyperbolic lattices.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37325",
  "author_total": 4,
  "authors": [
    {
      "name": "Pallabi Dey"
    },
    {
      "name": "Debasish Banerjee"
    },
    {
      "name": "Arnab Kundu"
    },
    {
      "name": "Ritam Sinha"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/638p85889001c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37325",
  "fulltext_url": null,
  "id": "638p85889001c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37325",
  "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",
      "cond-mat.str-el"
    ],
    [
      "arxiv",
      "hep-lat"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3104|Theoretical and Computational Physics"
    ]
  ],
  "openalex": "W7214910238",
  "pdf_url": "https://arxiv.org/pdf/2609.37325",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/638p85889001c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2609.37325",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37325"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-lat",
      "subfield": "high-energy"
    }
  ],
  "title": "Boundary Condition dependent Universality Classes on a Hyperbolic Lattice",
  "title_text": "Boundary Condition dependent Universality Classes on a Hyperbolic Lattice",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:31Z",
  "url": "https://research.draconitic.com/paper/638p85889001c",
  "venue": "arXiv",
  "versions": []
}