{
  "abstract": "We study a fourth-order variational model for two-dimensional frustrated ferromagnets with competing exchange interactions and an applied magnetic field of strength $H>0$. For every $H>1/4$, we prove that the energy admits minimizers in the topological classes $Q=\\pm1$ and that every minimizing sequence is precompact in $H^2$ modulo translations. The main difficulty is that spectral coercivity degenerates as $H\\downarrow1/4$. Using a Helmholtz circle-mean identity, we prove that the residual energy of every nonzero-degree configuration has a uniform positive lower bound, even at the degenerate endpoint. Together with a sphere-valued $H^2$-splitting construction, this provides a threshold-stable binding inequality and yields compactness throughout the coercive regime. We also identify $H=1/4$ as the sharp spectral threshold. Below it the energy is unbounded from below, whereas at the threshold nonzero-degree configurations retain a positive energy barrier and degree-zero Weyl sequences lose compactness. Finally, in the strong-field regime, rescaled minimizers approach those minimizers of the limiting functional that maximize the Dirichlet energy, while topological-charge and normalized-energy measures concentrate on the $H^{-1/4}$-scale.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08255",
  "author_total": 1,
  "authors": [
    {
      "name": "Xinye Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4cdmdm961qc4a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08255",
  "fulltext_url": null,
  "id": "4cdmdm961qc4a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08255",
  "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.AP"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7212085892",
  "pdf_url": "https://arxiv.org/pdf/2609.08255",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4cdmdm961qc4a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.08255",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08255"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Existence and strong-field asymptotics of skyrmions in a fourth-order model of frustrated ferromagnets",
  "title_text": "Existence and strong-field asymptotics of skyrmions in a fourth-order model of frustrated ferromagnets",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/4cdmdm961qc4a",
  "venue": "arXiv",
  "versions": []
}