{
  "abstract": "We study the statistical properties of passive and active many-body systems with orientational degrees of freedom on non-orientable domains. By rephrasing topological constraints as non-local symmetry relations on an orientable double-cover, we show that non-orientability eliminates global rotational soft modes without acting like an external field. In a passive XY model, this results in topological caging, where orientational fluctuations that exhibit conventional diffusive behavior on a torus saturate on a Klein bottle to a finite value that we compute exactly in the thermodynamic limit. In models of active self-propelled particles with orientational degrees of freedom, topological caging persists despite continuously changing interaction neighborhoods. In an active Ising spin model, non-orientability enforces the coexistence of ordered anti-parallel domains with vanishing global polar order, a state that is absent on orientable domains.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11367",
  "author_total": 4,
  "authors": [
    {
      "name": "Gianmarco Spera"
    },
    {
      "name": "Axel Fotso Ndefo"
    },
    {
      "name": "Keaton J. Burns"
    },
    {
      "name": "Alexander Mietke"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1ng5fpggnc37r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11367",
  "fulltext_url": null,
  "id": "1ng5fpggnc37r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11367",
  "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.soft"
    ],
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "openalex",
      "3104|Theoretical and Computational Physics"
    ]
  ],
  "openalex": "W7212280445",
  "pdf_url": "https://arxiv.org/pdf/2609.11367",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1ng5fpggnc37r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:26Z",
      "native_id": "2609.11367",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11367"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.soft",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Orientational order on non-orientable domains",
  "title_text": "Orientational order on non-orientable domains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:26Z",
  "url": "https://research.draconitic.com/paper/1ng5fpggnc37r",
  "venue": "arXiv",
  "versions": []
}