{
  "abstract": "On the $\\{5,4\\}$ hyperbolic lattice, the outermost generation holds 73\\% of the sites at all system sizes, making macroscopic averages strictly boundary-dependent. We study the ferromagnetic Ising model on this geometry with free boundaries by Monte Carlo simulation, demonstrating that conventional observables cease to identify a single critical scale. Instead, the finite lattices are organized by two distinct temperature scales. The susceptibility maximum identifies the lower transition scale at $T_{c2}=1.4782(15)J/k_{B}$ without extrapolation. However, the order-parameter distribution lacks a conventional fixed point at this scale. A distinct pseudocritical scale emerges instead at $T^{*}\\simeq1.67(3)$ inside the boundary-sensitive intermediate phase, where Binder cumulant curves cross and effective exponents are compatible with mean-field criticality. Between $T_{c2}$ and $T^{*}$, the interior amplifies boundary fluctuations into induced order. Furthermore, because the volume grows exponentially with depth, finite-size scaling must be formulated in the generation index rather than the total number of sites. The lack of asymptotic power-law convergence in the scaling stretch confirms through an independent observable that $T^{*}$ is a finite-size crossover rather than a thermodynamic fixed point. Finally, by applying a coherent field to the outermost generation alone, we recover the upper thermodynamic transition at $T_{pt}=2.81(1)J/k_{B}$, demonstrating that it remains accessible under an appropriate boundary perturbation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29323",
  "author_total": 4,
  "authors": [
    {
      "name": "Sebastian Jaroszewicz"
    },
    {
      "name": "Nahuel Mendez"
    },
    {
      "name": "Maria P. Beccar-Varela"
    },
    {
      "name": "Maria C. Mariani"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5d2t5yr05axbt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29323",
  "fulltext_url": null,
  "id": "5d2t5yr05axbt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29323",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "openalex",
      "3104|Theoretical and Computational Physics"
    ]
  ],
  "openalex": "W7214384977",
  "pdf_url": "https://arxiv.org/pdf/2609.29323",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5d2t5yr05axbt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:11Z",
      "native_id": "2609.29323",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29323"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Two temperature scales in the Ising model on the $\\{5,4\\}$ hyperbolic lattice with free boundaries: susceptibility peak and boundary-induced order",
  "title_text": "Two temperature scales in the Ising model on the {5,4} hyperbolic lattice with free boundaries: susceptibility peak and boundary-induced order",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:11Z",
  "url": "https://research.draconitic.com/paper/5d2t5yr05axbt",
  "venue": "arXiv",
  "versions": []
}