发表机构
University of Oxford; Massachusetts Institute of Technology; Flatiron Institute（牛津大学; 麻省理工学院; 平顿研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究不可定向域上取向自由度系统的统计性质，通过双覆盖方法揭示拓扑笼蔽效应，消除全局旋转软模，并在主动伊辛模型中强制反平行畴共存。
AI 中文摘要
我们研究了在不可定向域上具有取向自由度的被动和主动多体系统的统计性质。通过将拓扑约束重新表述为可定向双覆盖上的非局域对称关系，我们证明了不可定向性消除了全局旋转软模，而无需像外场那样作用。在被动XY模型中，这导致拓扑笼蔽效应，即在环面上表现出常规扩散行为的取向涨落，在克莱因瓶上饱和到一个有限值，我们在热力学极限下精确计算了该值。在具有取向自由度的主动自推进粒子模型中，尽管相互作用邻域不断变化，拓扑笼蔽效应仍然存在。在主动伊辛自旋模型中，不可定向性强制了有序反平行畴的共存，并伴随全局极序消失，这种状态在可定向域上是不存在的。
英文摘要
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.
Comments15 pages, 5 figures
