{
  "abstract": "Infrared singularities of gapless Goldstone modes preclude magnetic long-range order at finite temperature in conventional two-dimensional systems. By studying the spin-$S$ Heisenberg model on regular tilings of the hyperbolic plane, we show that this obstruction is absent in negatively curved space. Using spin-wave theory, we find that the zero-energy collective modes required by symmetry carry vanishing local spectral weight and are separated from the thermodynamic bulk magnon continuum by a finite gap in the bulk local spectral density. As a result, local transverse correlations remain short ranged, with a finite correlation length, despite the presence of Goldstone modes associated with the broken SO(3) spin-rotation symmetry. Stronger negative curvature is found to suppress quantum fluctuations in bulk thermodynamic quantities, pushing the ordered state toward \"mean-field-like\" behavior. We further estimate the ordering temperature from the thermal spin-wave correction to the ordered moment. These results establish hyperbolic geometry as a route to finite-temperature magnetic order that circumvents the Mermin-Wagner obstruction without breaking or modifying the continuous symmetry.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Phys. Rev. B 114, 134430 (2026)",
  "arxiv": "2606.27422",
  "author_total": 2,
  "authors": [
    {
      "name": "Alexander Hickey"
    },
    {
      "name": "Joseph Maciejko"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1j75eqeeq58xz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.27422",
  "fulltext_url": null,
  "id": "1j75eqeeq58xz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.27422",
  "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.str-el"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2606.27422",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1j75eqeeq58xz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:52Z",
      "native_id": "2606.27422",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.27422"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Magnetic long-range order at finite temperature in two-dimensional hyperbolic lattices",
  "title_text": "Magnetic long-range order at finite temperature in two-dimensional hyperbolic lattices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:52Z",
  "url": "https://research.draconitic.com/paper/1j75eqeeq58xz",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1103/bbzf-dzrc",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}