{
  "abstract": "We study a continuum model of frustrated magnetism that supports particle-like field configurations with nontrivial Hopf index. The energy functional combines competing second and first order exchange interactions with a stabilizing external magnetic field and gives rise to a variational problem for maps from three-dimensional space into the two-sphere. We prove the existence of energy minimizers in infinitely many nontrivial homotopy classes. We further establish the existence of a unit-charge Hopfion in the regime of strong external fields. Finally, we analyze the corresponding large-field limit, identify the natural concentration scale, and prove strong convergence of suitably rescaled minimizers to a minimizer of a limiting variational problem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13883",
  "author_total": 2,
  "authors": [
    {
      "name": "Glal Bacho"
    },
    {
      "name": "Christof Melcher"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/300b79efb1xj7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13883",
  "fulltext_url": null,
  "id": "300b79efb1xj7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13883",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7221551574",
  "pdf_url": "https://arxiv.org/pdf/2610.13883",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/300b79efb1xj7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:36Z",
      "native_id": "2610.13883",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13883"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Existence and large-field asymptotics of Hopfions in a continuum model of frustrated magnets",
  "title_text": "Existence and large-field asymptotics of Hopfions in a continuum model of frustrated magnets",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/300b79efb1xj7",
  "venue": "arXiv",
  "versions": []
}