{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T23:51:06Z","timestamp":1791503466751,"version":"4.3.4"},"reference-count":84,"publisher":"American Physical Society (APS)","issue":"11","license":[{"start":{"date-parts":[[2026,9,9]],"date-time":"2026-09-09T00:00:00Z","timestamp":1788912000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000761","name":"Imperial College London","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000761","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. Lett."],"accepted":{"date-parts":[[2026,2,19]]},"abstract":"<jats:p>A hallmark in natural systems, self-organization often stems from very simple interaction rules between individual agents. While single-species self-propelled particle systems are well understood, the behavior of binary mixtures with general alignment interactions remains largely unexplored with a few scattered results hinting at the existence of a rich emergent phase behavior. Here, we investigate systematically a generalization of the two-species Vicsek model with reciprocal intra- and interspecies (anti)alignment couplings, uncovering a rich phenomenology of emergent states. Notably, we show that rather than destroying polar order, antialigning interactions can promote phase separation and the emergence of global polar order. In doing so, we uncover a novel mechanism for microphase separation. We further find these coexistence patterns can be generalized to multispecies systems with cyclic alignment interactions.<\/jats:p>","DOI":"10.1103\/lt6f-yjpd","type":"journal-article","created":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T20:22:23Z","timestamp":1771532543000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Flocking Beyond One Species: Novel Phase Coexistence in a Generalized Two-Species Vicsek Model"],"prefix":"10.1103","volume":"137","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-3602-3646","authenticated-orcid":true,"given":"Eloise","family":"Lardet","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/041kmwe10","id-type":"ROR","asserted-by":"publisher"}],"name":"Imperial College London"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-7015-5737","authenticated-orcid":true,"given":"Letian","family":"Chen","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/041kmwe10","id-type":"ROR","asserted-by":"publisher"}],"name":"Imperial College London"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9812-7904","authenticated-orcid":true,"given":"Thibault","family":"Bertrand","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/041kmwe10","id-type":"ROR","asserted-by":"publisher"}],"name":"Imperial College London"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"16","published-online":{"date-parts":[[2026,9,9]]},"reference":[{"key":"lt6f-yjpdCc1R1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.85.1143","type":"journal-article"},{"key":"lt6f-yjpdCc2R1","doi-asserted-by":"publisher","DOI":"10.1146\/annurev-conmatphys-070909-104101","type":"journal-article"},{"key":"lt6f-yjpdCc3R1","doi-asserted-by":"publisher","DOI":"10.2976\/1.2961038","type":"journal-article"},{"key":"lt6f-yjpdCc4R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2012.03.004","type":"journal-article"},{"key":"lt6f-yjpdCc5R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.108.098102","type":"journal-article"},{"key":"lt6f-yjpdCc6R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2017.11.003","type":"journal-article"},{"key":"lt6f-yjpdCc7R1","doi-asserted-by":"publisher","DOI":"10.1126\/science.aao5434","type":"journal-article"},{"key":"lt6f-yjpdCc8R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.103.032413","type":"journal-article"},{"key":"lt6f-yjpdCc9R1","volume-title":"Active Particles, Volume\u00a03: Advances in Theory, Models, and Applications","author":"G. 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model is referred to as the additive sine model in the absence of a normalization of the alignment interactions by the number of neighbors [27, 70].","type":"other"},{"key":"lt6f-yjpdCc70R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.104.044605","type":"journal-article"},{"key":"lt6f-yjpdCc71R1","unstructured":"Note that the interaction torques themselves may not be reciprocal; as particles may have different numbers of interaction neighbors ni, the alignment interactions are generically nonreciprocal in this mean-sine alignment rules. Refer to [27] for a discussion of this difference.","type":"other"},{"key":"lt6f-yjpdCc72R1","unstructured":"See Supplemental Material at http:\/\/link.aps.org\/supplemental\/10.1103\/lt6f-yjpd for further analytical and computational details, including videos, which includes Refs.\u00a0[46,73].","type":"other"},{"key":"lt6f-yjpdCc73R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2018.03.001","type":"journal-article"},{"key":"lt6f-yjpdCc74R1","doi-asserted-by":"publisher","DOI":"10.1103\/w9pf-3r76","type":"journal-article"},{"key":"lt6f-yjpdCc75R1","unstructured":"Note that we only sketched a single column of particles for illustration purposes, when in reality there are potentially hundreds of particles clustered in each stripe.","type":"other"},{"key":"lt6f-yjpdCc76R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-023-40241-w","type":"journal-article"},{"key":"lt6f-yjpdCc77R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-023-42713-5","type":"journal-article"},{"key":"lt6f-yjpdCc78R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.10.041009","type":"journal-article"},{"key":"lt6f-yjpdCc79R1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2010318117","type":"journal-article"},{"key":"lt6f-yjpdCc80R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.131.258301","type":"journal-article"},{"key":"lt6f-yjpdCc81R1","doi-asserted-by":"publisher","DOI":"10.1103\/qjl4-wqvx","type":"journal-article"},{"key":"lt6f-yjpdCc82R1","doi-asserted-by":"publisher","DOI":"10.1209\/0295-5075\/131\/68001","type":"journal-article"},{"key":"lt6f-yjpdCc83R1","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/acfdc2","type":"journal-article"},{"key":"lt6f-yjpdCc84R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.131.128301","type":"journal-article"},{"key":"lt6f-yjpdCc85R1","doi-asserted-by":"publisher","DOI":"10.7566\/JPSJ.95.013001","type":"journal-article"},{"key":"lt6f-yjpdCc86R1","doi-asserted-by":"publisher","DOI":"10.5281\/zenodo.18713863","type":"dataset"}],"container-title":["Physical Review Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.aps.org\/article\/10.1103\/lt6f-yjpd","content-type":"unspecified","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/harvest.aps.org\/v2\/journals\/articles\/10.1103\/lt6f-yjpd\/fulltext","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,9]],"date-time":"2026-09-09T16:32:44Z","timestamp":1788971564000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.aps.org\/doi\/10.1103\/lt6f-yjpd"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,9]]},"references-count":84,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2026,9]]}},"URL":"https:\/\/doi.org\/10.1103\/lt6f-yjpd","relation":{"has-preprint":[{"id-type":"doi","id":"10.48550\/arXiv.2503.17617","asserted-by":"subject"}]},"ISSN":["0031-9007","1079-7114"],"issn-type":[{"value":"0031-9007","type":"print"},{"value":"1079-7114","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,9]]},"assertion":[{"value":"2025-04-10","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"Published by the American Physical Society. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright_statement","label":"Copyright statement","group":{"name":"copyright","label":"copyright"}},{"value":"2026","name":"copyright_year","label":"Copyright year","group":{"name":"copyright","label":"copyright"}},{"value":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/","name":"creative_commons_license","label":"Creative Commons license","group":{"name":"licenses","label":"Licenses"}},{"value":"\u00a92026 The authors","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"118303"}}