{
  "abstract": "Every crystal is a Bravais lattice decorated by a basis, so the dipolar ordering of the fourteen Bravais lattices is the natural starting point for any systematic theory of dipolar magnetism in three dimensions. We determine it here in a single common framework: the interaction tensor is Ewald-summed, the classical ground state is obtained by minimising the lowest Luttinger--Tisza band over the entire Brillouin zone, and the linear spin-wave spectrum with its zero-point corrections is computed for every lattice whose order is collinear. Three results emerge that are not properties of individual lattices but of the landscape. First, two structural principles --- the exact tracelessness of the dipolar tensor in three dimensions, and its identical vanishing at $\\mathbf k=0$ for every cubic-symmetric lattice --- explain the ordering type, the absence of first-order cubic anisotropy, and the systematics of the zero-point moment reduction. Second, exactly one lattice defeats the Luttinger--Tisza construction: for face-centred orthorhombic the optimal eigenvector is not circular, the single-$\\mathbf k$ state is a spin-density wave of non-constant length, and the tabulated energy is a strict lower bound; direct supercell minimisation gives the true ground state. Third, optimising each family over its free metric parameters collapses the whole of Bravais space onto only \\emph{four} attractors, with body-centred tetragonal the global optimum and a single interior optimum at rhombohedral $α=62.42^\\circ$ lying below face-centred cubic. Three independent published benchmarks are reproduced.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02936",
  "author_total": 1,
  "authors": [
    {
      "name": "Josep Batle"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ayy42p91pfahq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02936",
  "fulltext_url": null,
  "id": "ayy42p91pfahq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02936",
  "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",
      "cond-mat.stat-mech"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.02936",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ayy42p91pfahq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:31Z",
      "native_id": "2609.02936",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02936"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Dipolar order across Bravais lattice space: classification, spin waves, and a four-attractor phase diagram",
  "title_text": "Dipolar order across Bravais lattice space: classification, spin waves, and a four-attractor phase diagram",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:31Z",
  "url": "https://research.draconitic.com/paper/ayy42p91pfahq",
  "venue": "arXiv",
  "versions": []
}