{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T23:55:29Z","timestamp":1740182129998,"version":"3.37.3"},"reference-count":53,"publisher":"The Royal Society","issue":"2171","license":[{"start":{"date-parts":[[2020,4,13]],"date-time":"2020-04-13T00:00:00Z","timestamp":1586736000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/royalsociety.org\/journals\/ethics-policies\/data-sharing-mining\/"}],"funder":[{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"crossref","award":["19-42-04120"],"award-info":[{"award-number":["19-42-04120"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["royalsocietypublishing.org"],"crossmark-restriction":true},"short-container-title":["Phil. Trans. R. Soc. A."],"published-print":{"date-parts":[[2020,5,15]]},"abstract":"<jats:p>\n            The problem of magnetic transitions between the low-temperature (macrospin ordered) phases in two-dimensional XY arrays is addressed. The system is modelled as a plane structure of identical single-domain particles arranged in a square lattice and coupled by the magnetic dipole\u2013dipole interaction; all the particles possess a strong easy-plane magnetic anisotropy. The basic state of the system in the considered temperature range is an antiferromagnetic (AF) stripe structure, where the macrospins (particle magnetic moments) are still involved in thermofluctuational motion: the superparamagnetic blocking\n            <jats:italic>T<\/jats:italic>\n            <jats:sub>\n              <jats:italic>b<\/jats:italic>\n            <\/jats:sub>\n            temperature is lower than that (\n            <jats:italic>T<\/jats:italic>\n            <jats:sub>af<\/jats:sub>\n            ) of the AF transition. The description is based on the stochastic equations governing the dynamics of individual magnetic moments, where the interparticle interaction is added in the mean-field approximation. With the technique of a generalized Ott\u2013Antonsen theory, the dynamics equations for the order parameters (including the macroscopic magnetization and the AF order parameter) and the partition function of the system are rigorously obtained and analysed. We show that inside the temperature interval of existence of the AF phase, a static external field tilted to the plane of the array is able to induce first-order phase transitions from AF to ferromagnetic state; the phase diagrams displaying stable and metastable regions of the system are presented.\n          <\/jats:p>\n          <jats:p>This article is part of the theme issue \u2018Patterns in soft and biological matters\u2019.<\/jats:p>","DOI":"10.1098\/rsta.2019.0259","type":"journal-article","created":{"date-parts":[[2020,4,12]],"date-time":"2020-04-12T23:05:52Z","timestamp":1586732752000},"page":"20190259","update-policy":"https:\/\/doi.org\/10.1098\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Collective in-plane magnetization in a two-dimensional XY macrospin system within the framework of generalized Ott\u2013Antonsen theory"],"prefix":"10.1098","volume":"378","author":[{"given":"Irina V.","family":"Tyulkina","sequence":"first","affiliation":[{"name":"Institute of Continuous Media Mechanics, UB RAS, Academician Korolev Street 1, Perm 614068, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Denis S.","family":"Goldobin","sequence":"additional","affiliation":[{"name":"Institute of Continuous Media Mechanics, UB RAS, Academician Korolev Street 1, Perm 614068, Russia"},{"name":"Department of Theoretical Physics, Perm State University, Bukirev Street 15, Perm 614990, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lyudmila S.","family":"Klimenko","sequence":"additional","affiliation":[{"name":"Institute of Continuous Media Mechanics, UB RAS, Academician Korolev Street 1, Perm 614068, Russia"},{"name":"Department of Theoretical Physics, Perm State University, Bukirev Street 15, Perm 614990, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Igor S.","family":"Poperechny","sequence":"additional","affiliation":[{"name":"Institute of Continuous Media Mechanics, UB RAS, Academician Korolev Street 1, Perm 614068, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6167-6528","authenticated-orcid":true,"given":"Yuriy L.","family":"Raikher","sequence":"additional","affiliation":[{"name":"Institute of Continuous Media Mechanics, UB RAS, Academician Korolev Street 1, Perm 614068, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"175","published-online":{"date-parts":[[2020,4,13]]},"reference":[{"key":"e_1_3_6_2_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.4891479"},{"key":"e_1_3_6_3_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-018-05216-2"},{"key":"e_1_3_6_4_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.120.264101"},{"key":"e_1_3_6_5_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.2930766"},{"key":"e_1_3_6_6_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.3136851"},{"volume-title":"Chemical oscillations, waves and turbulence","year":"2003","author":"Kuramoto Y","key":"e_1_3_6_7_2"},{"key":"e_1_3_6_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-010-0217-2"},{"key":"e_1_3_6_9_2","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2018.0467"},{"key":"e_1_3_6_10_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.70.2391"},{"key":"e_1_3_6_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(94)90196-1"},{"key":"e_1_3_6_12_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.101.264103"},{"key":"e_1_3_6_13_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.3247089"},{"key":"e_1_3_6_14_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.3087132"},{"key":"e_1_3_6_15_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.90.010901"},{"key":"e_1_3_6_16_2","first-page":"011009","article-title":"Low-dimensional dynamics of populations of pulse-coupled oscillators","volume":"4","author":"Paz\u00f3 D","year":"2014","journal-title":"Phys. Rev. X"},{"key":"e_1_3_6_17_2","first-page":"021028","article-title":"Macroscopic description for networks of spiking neurons","volume":"5","author":"Montbri\u00f3 E","year":"2015","journal-title":"Phys. Rev. X"},{"key":"e_1_3_6_18_2","doi-asserted-by":"publisher","DOI":"10.3389\/fncom.2014.00145"},{"key":"e_1_3_6_19_2","doi-asserted-by":"publisher","DOI":"10.1186\/s13408-018-0059-7"},{"key":"e_1_3_6_20_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.96.062204"},{"key":"e_1_3_6_21_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.100.062211"},{"key":"e_1_3_6_22_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.101.084103"},{"key":"e_1_3_6_23_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.92.050904"},{"key":"e_1_3_6_24_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2009.04.012"},{"key":"e_1_3_6_25_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.82.035205"},{"key":"e_1_3_6_26_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.4870259"},{"key":"e_1_3_6_27_2","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8121\/aa55f1"},{"key":"e_1_3_6_28_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.98.062222"},{"key":"e_1_3_6_29_2","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8121\/ab0043"},{"key":"e_1_3_6_30_2","doi-asserted-by":"publisher","DOI":"10.1137\/16M1086662"},{"key":"e_1_3_6_31_2","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6544\/aaaa07"},{"key":"e_1_3_6_32_2","doi-asserted-by":"publisher","DOI":"10.1038\/srep38518"},{"key":"e_1_3_6_33_2","doi-asserted-by":"publisher","DOI":"10.1140\/epjst\/e2017-70039-y"},{"key":"e_1_3_6_34_2","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2019.0041"},{"key":"e_1_3_6_35_2","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2019.0092"},{"key":"e_1_3_6_36_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2019.03.026"},{"key":"e_1_3_6_37_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.1.033139"},{"key":"e_1_3_6_38_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11141-019-09924-7"},{"key":"e_1_3_6_39_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0219477519400029"},{"key":"e_1_3_6_40_2","first-page":"153","article-title":"On the theory of the dispersion of the magnetic permeability of ferromagnetic bodies","volume":"8","author":"Landau LD","year":"1935","journal-title":"Phys. Z. Sowjetunion"},{"volume-title":"Ferromagnetic resonance","year":"1966","author":"Vonsovskii SV","key":"e_1_3_6_41_2"},{"key":"e_1_3_6_42_2","doi-asserted-by":"publisher","DOI":"10.1109\/TMAG.2004.836740"},{"key":"e_1_3_6_43_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.83.34"},{"key":"e_1_3_6_44_2","doi-asserted-by":"publisher","DOI":"10.1002\/andp.19053220806"},{"key":"e_1_3_6_45_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(79)90152-9"},{"key":"e_1_3_6_46_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.4766596"},{"key":"e_1_3_6_47_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.4963371"},{"key":"e_1_3_6_48_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.5053576"},{"key":"e_1_3_6_49_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.100.052211"},{"key":"e_1_3_6_50_2","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8121\/ab6b90"},{"key":"e_1_3_6_51_2","doi-asserted-by":"publisher","DOI":"10.1201\/9781315119472"},{"key":"e_1_3_6_52_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.3048415"},{"volume-title":"Magnetism","year":"1974","author":"Vonsovskii SV","key":"e_1_3_6_53_2"},{"key":"e_1_3_6_54_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-009-9908-9"}],"container-title":["Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/royalsocietypublishing.org\/doi\/pdf\/10.1098\/rsta.2019.0259","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/royalsocietypublishing.org\/doi\/full-xml\/10.1098\/rsta.2019.0259","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/royalsocietypublishing.org\/doi\/pdf\/10.1098\/rsta.2019.0259","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,17]],"date-time":"2021-02-17T17:39:12Z","timestamp":1613583552000},"score":1,"resource":{"primary":{"URL":"https:\/\/royalsocietypublishing.org\/doi\/10.1098\/rsta.2019.0259"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,13]]},"references-count":53,"journal-issue":{"issue":"2171","published-print":{"date-parts":[[2020,5,15]]}},"alternative-id":["10.1098\/rsta.2019.0259"],"URL":"https:\/\/doi.org\/10.1098\/rsta.2019.0259","relation":{},"ISSN":["1364-503X","1471-2962"],"issn-type":[{"type":"print","value":"1364-503X"},{"type":"electronic","value":"1471-2962"}],"subject":[],"published":{"date-parts":[[2020,4,13]]},"assertion":[{"value":"2020-01-22","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2020-04-13","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}