Universal structural mechanism underlying collective order in active matter

Universal structural mechanism underlying collective order in active matter | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Universal structural mechanism underlying collective order in active matter Kejun Dong, Ruizhi Jin This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8051267/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract How collective order in active matter arises from simple local interactions remains a central and fascinating question. While previous theories have primarily focused on how control parameters drive ordering, the underlying structural mechanisms remain elusive. Here, we uncover a universal structure–order relationship in Vicsek systems: across a range of densities and noise strengths, the polar order parameter exhibits a general correlation with the average interaction number. This relationship reconciles the apparently distinct order transitions induced by different control parameters within a unified framework of structure–order evolution, comprising four stages: disorder, order growth, order coherence, and order saturation. We further identify scale-invariant cluster structures and demonstrate that both cluster-level and system-level degree distributions converge toward a universal form, and similar cluster structures are identified in starling flocks. Building on these structural universalities, we develop a theoretical framework that predicts the order parameter from structural statistics, highlighting the vital role of structural evolution in the onset, growth, and saturation of the order parameter. This work provides a new structural perspective on the disorder–order transition of Vicsek systems and suggests new principles for understanding and engineering collective behavior in active matter. Physical sciences/Physics/Statistical physics, thermodynamics and nonlinear dynamics/Phase transitions and critical phenomena Physical sciences/Physics/Biological physics Physical sciences/Physics/Statistical physics, thermodynamics and nonlinear dynamics/Complex networks Full Text Additional Declarations There is NO Competing Interest. Supplementary Files Supplemetarymaterial.docx Supplementary Information for "Universal structural mechanism underlying collective order in active matter" Cite Share Download PDF Status: Under Review Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8051267","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":545058415,"identity":"1f7e4168-0948-41db-86db-bbca5dbf12bd","order_by":0,"name":"Kejun 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