{
  "abstract": "We study the full nonlinear mean-field Landau--Lifshitz--Bloch equation in micromagnetics arising from Garanin's spin-polarisation model [D. Garanin. Fokker-Planck and Landau-Lifshitz-Bloch equations for classical ferromagnets. Phys. Rev. B, 55 (1997)] prior to the usual near-equilibrium reduction. The equation combines a singular inverse-Langevin potential with a mobility whose longitudinal component degenerates at saturation, together with exchange, anisotropy, and the nonlocal whole-space stray field. The natural state space is the closed unit ball $|m|\\leq 1$. For any $H^1$ initial data satisfying $|m_0|\\leq1$, including saturated data of infinite free energy, we construct global weak solutions and derive instantaneous separation from saturation $|m|=1$. This restores uniform parabolicity and yields the thermodynamic formulation and exact energy identity for positive times. We further establish a quantitative low-temperature limit to the Landau--Lifshitz--Gilbert equation and prove convergence of global trajectories to a single equilibrium. A spectral Curie-type threshold characterises the stability of the paramagnetic state and yields exponential relaxation above the threshold. Finally, for uniformly separated data we prove strong well-posedness, including global strong solutions in one- and two-dimensional domains, and exponential stability of non-degenerate equilibria, with a small-data global theory in three dimensions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00365",
  "author_total": 1,
  "authors": [
    {
      "name": "Agus L. Soenjaya"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8dy8qw9b81pzs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00365",
  "fulltext_url": null,
  "id": "8dy8qw9b81pzs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00365",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00365",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8dy8qw9b81pzs.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00365",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00365"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Beyond the reduced Landau--Lifshitz--Bloch equation: Singular potential, global well-posedness, and micromagnetic limits",
  "title_text": "Beyond the reduced Landau--Lifshitz--Bloch equation: Singular potential, global well-posedness, and micromagnetic limits",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/8dy8qw9b81pzs",
  "venue": "arXiv",
  "versions": []
}