Asphericity Lifts the Degeneracy Among Ordering Mechanisms on Curved Surfaces

[2608.27520] Asphericity lifts the degeneracy among ordering mechanisms on curved surfaces Skip to main content Search Submit Donate Log in Condensed Matter > Soft Condensed Matter arXiv:2608.27520 (cond-mat) [Submitted on 27 Aug 2026 ( v1 ), last revised 1 Oct 2026 (this version, v2)] Title: Asphericity lifts the degeneracy among ordering mechanisms on curved surfaces Authors: Anže Božič View PDF HTML (experimental) Abstract: Spherical surfaces conceal the one-body signature of particle organization: area-uniform, conductor, and curvature-weighted measures coincide there, so the ordering mechanism leaves no trace in the density. Hard spheres and Coulomb charges confined to the sphere thus produce identical mean densities, and distinctions between their particle arrangements appear only in many-body correlations. Aspherical deformation lifts this degeneracy, and we show that on an ellipsoid, different ordering mechanisms separate by virtue of a single exponent $p$ of the distance from the shell center to its tangent plane. To leading order in deformation, the characteristic exponent $p$ can be obtained both from the quadrupole of the spherical structure factor and from the radius of gyration. Two interaction families demonstrate how this can be realized in practice: the Riesz $s$-energy, whose limiting measure is determined by the power $s$ and exhibits a transition at $s=d=2$, and the screened Coulomb potential, whose measure and thus the characteristic exponent are tuned continuously by the salt concentration. The value of the characteristic exponent $p$ positions the arrangement of particles between the conductor and packing limits, and its response to a control parameter such as salt concentration can be used experimentally to identify the interaction family. Comments: 10 pages, 3 figures Subjects: Soft Condensed Matter (cond-mat.soft) Cite as: arXiv:2608.27520 [cond-mat.soft] (or arXiv:2608.27520v2 [cond-mat.soft] for this version) https://doi.org/10.48550/arXiv.2608.27520 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Anze Bozic [ view email ] [v1] Thu, 27 Aug 2026 12:42:56 UTC (1,085 KB) [v2] Thu, 1 Oct 2026 15:25:42 UTC (1,090 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: cond-mat.soft < prev | next > new | recent | 2026-08 Change to browse by: cond-mat References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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