Orientational order on non-orientable domains

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.

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BibTeX RIS

BibTeX

@misc{spera2026orientational,
  title = {{Orientational order on non-orientable domains}},
  author = {Gianmarco Spera and Axel Fotso Ndefo and Keaton J. Burns and Alexander Mietke},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.11367},
  eprint = {2609.11367},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.11367},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Orientational order on non-orientable domains
AU  - Gianmarco Spera
AU  - Axel Fotso Ndefo
AU  - Keaton J. Burns
AU  - Alexander Mietke
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.11367
UR  - https://arxiv.org/abs/2609.11367
AB  - 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.
ER  -

Abstract

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