{"id":"https://openalex.org/W7214726658","doi":"https://doi.org/10.48550/arxiv.2609.32644","title":"Finite-temperature phase transitions across spin symmetries in two-dimensional magnets","display_name":"Finite-temperature phase transitions across spin symmetries in two-dimensional magnets","publication_year":2026,"publication_date":"2026-09-26","ids":{"openalex":"https://openalex.org/W7214726658","doi":"https://doi.org/10.48550/arxiv.2609.32644"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.32644","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.32644","pdf_url":"https://arxiv.org/pdf/2609.32644","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.32644","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159964291","display_name":"Chen Chen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I36399199","display_name":"Nanjing University of Science and Technology","ror":"https://ror.org/00xp9wg62","country_code":"CN","type":"education","lineage":["https://openalex.org/I36399199"]},{"id":"https://openalex.org/I4210135147","display_name":"Centre d\u2019\u00c9laboration de Mat\u00e9riaux et d\u2019\u00c9tudes Structurales","ror":"https://ror.org/03kwnqq69","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I196454796","https://openalex.org/I4210098836","https://openalex.org/I4210135147","https://openalex.org/I4405258862"]},{"id":"https://openalex.org/I4405258862","display_name":"Universit\u00e9 de Toulouse","ror":"https://ror.org/01ahyrz84","country_code":"FR","type":"education","lineage":["https://openalex.org/I4405258862"]}],"countries":["CN","FR"],"is_corresponding":false,"raw_author_name":"Chen, Chen","raw_affiliation_strings":["Department of Applied Physics and MIIT Key Laboratory of Semiconductor Microstructure and Quantum Sensing , Nanjing University of Science and Technology , Nanjing , China","Universit\u00e9 de Toulouse , CNRS , CEMES , Toulouse , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Physics and MIIT Key Laboratory of Semiconductor Microstructure and Quantum Sensing , Nanjing University of Science and Technology , Nanjing , China","institution_ids":["https://openalex.org/I36399199"]},{"raw_affiliation_string":"Universit\u00e9 de Toulouse , CNRS , CEMES , Toulouse , France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210135147","https://openalex.org/I4405258862"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020697266","display_name":"Moritz A. Goerzen","orcid":"https://orcid.org/0000-0001-6591-3829","observed_orcids":["https://orcid.org/0000-0001-6591-3829"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210135147","display_name":"Centre d\u2019\u00c9laboration de Mat\u00e9riaux et d\u2019\u00c9tudes Structurales","ror":"https://ror.org/03kwnqq69","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I196454796","https://openalex.org/I4210098836","https://openalex.org/I4210135147","https://openalex.org/I4405258862"]},{"id":"https://openalex.org/I4405258862","display_name":"Universit\u00e9 de Toulouse","ror":"https://ror.org/01ahyrz84","country_code":"FR","type":"education","lineage":["https://openalex.org/I4405258862"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Goerzen, Moritz A.","raw_affiliation_strings":["Universit\u00e9 de Toulouse , CNRS , CEMES , Toulouse , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Toulouse , CNRS , CEMES , Toulouse , France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210135147","https://openalex.org/I4405258862"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028878131","display_name":"Megha Arya","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210135147","display_name":"Centre d\u2019\u00c9laboration de Mat\u00e9riaux et d\u2019\u00c9tudes Structurales","ror":"https://ror.org/03kwnqq69","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I196454796","https://openalex.org/I4210098836","https://openalex.org/I4210135147","https://openalex.org/I4405258862"]},{"id":"https://openalex.org/I4405258862","display_name":"Universit\u00e9 de Toulouse","ror":"https://ror.org/01ahyrz84","country_code":"FR","type":"education","lineage":["https://openalex.org/I4405258862"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Arya, Megha","raw_affiliation_strings":["Universit\u00e9 de Toulouse , CNRS , CEMES , Toulouse , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Toulouse , CNRS , CEMES , Toulouse , France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210135147","https://openalex.org/I4405258862"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030045433","display_name":"L. Calmels","orcid":"https://orcid.org/0000-0002-0532-0404","observed_orcids":["https://orcid.org/0000-0002-0532-0404"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210135147","display_name":"Centre d\u2019\u00c9laboration de Mat\u00e9riaux et d\u2019\u00c9tudes Structurales","ror":"https://ror.org/03kwnqq69","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I196454796","https://openalex.org/I4210098836","https://openalex.org/I4210135147","https://openalex.org/I4405258862"]},{"id":"https://openalex.org/I4405258862","display_name":"Universit\u00e9 de Toulouse","ror":"https://ror.org/01ahyrz84","country_code":"FR","type":"education","lineage":["https://openalex.org/I4405258862"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Calmels, Lionel","raw_affiliation_strings":["Universit\u00e9 de Toulouse , CNRS , CEMES , Toulouse , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Toulouse , CNRS , CEMES , Toulouse , France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210135147","https://openalex.org/I4405258862"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5153476375","display_name":"Yongping Du","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I36399199","display_name":"Nanjing University of Science and Technology","ror":"https://ror.org/00xp9wg62","country_code":"CN","type":"education","lineage":["https://openalex.org/I36399199"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Du, Yongping","raw_affiliation_strings":["Department of Applied Physics and MIIT Key Laboratory of Semiconductor Microstructure and Quantum Sensing , Nanjing University of Science and Technology , Nanjing , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Physics and MIIT Key Laboratory of Semiconductor Microstructure and Quantum Sensing , Nanjing University of Science and Technology , Nanjing , China","institution_ids":["https://openalex.org/I36399199"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025374486","display_name":"Dongzhe Li","orcid":"https://orcid.org/0000-0003-0929-8125","observed_orcids":["https://orcid.org/0000-0003-0929-8125"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210135147","display_name":"Centre d\u2019\u00c9laboration de Mat\u00e9riaux et d\u2019\u00c9tudes Structurales","ror":"https://ror.org/03kwnqq69","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I196454796","https://openalex.org/I4210098836","https://openalex.org/I4210135147","https://openalex.org/I4405258862"]},{"id":"https://openalex.org/I4405258862","display_name":"Universit\u00e9 de Toulouse","ror":"https://ror.org/01ahyrz84","country_code":"FR","type":"education","lineage":["https://openalex.org/I4405258862"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Li, Dongzhe","raw_affiliation_strings":["Universit\u00e9 de Toulouse , CNRS , CEMES , Toulouse , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Toulouse , CNRS , CEMES , Toulouse , France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210135147","https://openalex.org/I4405258862"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.9883000254631042,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.9883000254631042,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11682","display_name":"Advanced Condensed Matter Physics","score":0.007199999876320362,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10037","display_name":"Physics of Superconductivity and Magnetism","score":0.0010999999940395355,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/two-dimensional-magnetic-materials","display_name":"two-dimensional magnets","score":0.8259999752044678},{"id":"https://openalex.org/keywords/finite-temperature-phase-transition","display_name":"finite-temperature phase transition","score":0.843999981880188},{"id":"https://openalex.org/keywords/heisenberg-model","display_name":"Heisenberg model","score":0.8220000267028809},{"id":"https://openalex.org/keywords/spin-symmetry","display_name":"spin symmetry","score":0.7570000290870667},{"id":"https://openalex.org/keywords/isotropic-heisenberg-model","display_name":"isotropic Heisenberg model","score":0.75},{"id":"https://openalex.org/keywords/berezinskii-kosterlitz-thouless-transition","display_name":"Kosterlitz-Thouless transition","score":0.9380000233650208},{"id":"https://openalex.org/keywords/vortex-antivortex-pairs","display_name":"vortex-antivortex pairs","score":0.902999997138977},{"id":"https://openalex.org/keywords/vortex-nucleation","display_name":"vortex nucleation","score":0.7279999852180481},{"id":"https://openalex.org/keywords/magnetocrystalline-anisotropy","display_name":"magnetocrystalline anisotropy","score":0.8980000019073486},{"id":"https://openalex.org/keywords/finite-size-effects","display_name":"finite-size effects","score":0.9409999847412109},{"id":"https://openalex.org/keywords/heat-capacity","display_name":"heat capacity","score":0.7860000133514404},{"id":"https://openalex.org/keywords/magnetization","display_name":"magnetization","score":0.7689999938011169},{"id":"https://openalex.org/keywords/spin-correlations","display_name":"spin correlations","score":0.4410000145435333},{"id":"https://openalex.org/keywords/xy-model","display_name":"XY model","score":0.5220000147819519}],"concepts":[{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.7258999943733215},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6331999897956848},{"id":"https://openalex.org/C197162081","wikidata":"https://www.wikidata.org/wiki/Q3294789","display_name":"Magnetism","level":2,"score":0.5935999751091003},{"id":"https://openalex.org/C201665358","wikidata":"https://www.wikidata.org/wiki/Q899196","display_name":"Heisenberg model","level":3,"score":0.5504999756813049},{"id":"https://openalex.org/C16389437","wikidata":"https://www.wikidata.org/wiki/Q11421","display_name":"Magnet","level":2,"score":0.5030999779701233},{"id":"https://openalex.org/C42704618","wikidata":"https://www.wikidata.org/wiki/Q910917","display_name":"Spin (aerodynamics)","level":2,"score":0.4880000054836273},{"id":"https://openalex.org/C149288129","wikidata":"https://www.wikidata.org/wiki/Q185357","display_name":"Phase transition","level":2,"score":0.48240000009536743},{"id":"https://openalex.org/C32546565","wikidata":"https://www.wikidata.org/wiki/Q856711","display_name":"Magnetization","level":3,"score":0.47540000081062317},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.4489000141620636},{"id":"https://openalex.org/C61048295","wikidata":"https://www.wikidata.org/wiki/Q909022","display_name":"Nucleation","level":2,"score":0.4052000045776367},{"id":"https://openalex.org/C12997251","wikidata":"https://www.wikidata.org/wiki/Q567560","display_name":"Anomaly (physics)","level":2,"score":0.39500001072883606},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.39309999346733093},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.3910999894142151},{"id":"https://openalex.org/C2986087423","wikidata":"https://www.wikidata.org/wiki/Q487756","display_name":"Specific heat","level":2,"score":0.385699987411499},{"id":"https://openalex.org/C85906118","wikidata":"https://www.wikidata.org/wiki/Q186693","display_name":"Phase diagram","level":3,"score":0.38420000672340393},{"id":"https://openalex.org/C25949731","wikidata":"https://www.wikidata.org/wiki/Q904675","display_name":"Spin ice","level":3,"score":0.3806999921798706},{"id":"https://openalex.org/C2780198381","wikidata":"https://www.wikidata.org/wiki/Q17083882","display_name":"Spin model","level":2,"score":0.373199999332428},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.35749998688697815},{"id":"https://openalex.org/C51329190","wikidata":"https://www.wikidata.org/wiki/Q1076349","display_name":"Ising model","level":2,"score":0.3547999858856201},{"id":"https://openalex.org/C82217956","wikidata":"https://www.wikidata.org/wiki/Q184207","display_name":"Ferromagnetism","level":2,"score":0.3450999855995178},{"id":"https://openalex.org/C140820882","wikidata":"https://www.wikidata.org/wiki/Q732722","display_name":"Vortex","level":2,"score":0.32359999418258667},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.32120001316070557},{"id":"https://openalex.org/C23792430","wikidata":"https://www.wikidata.org/wiki/Q1122780","display_name":"Superparamagnetism","level":4,"score":0.29660001397132874},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.29510000348091125},{"id":"https://openalex.org/C115260700","wikidata":"https://www.wikidata.org/wiki/Q11408","display_name":"Magnetic field","level":2,"score":0.2759999930858612},{"id":"https://openalex.org/C194807282","wikidata":"https://www.wikidata.org/wiki/Q900634","display_name":"Critical phenomena","level":3,"score":0.26440000534057617},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.2535000145435333}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.32644","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.32644","pdf_url":"https://arxiv.org/pdf/2609.32644","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.32644","doi":"https://doi.org/10.48550/arxiv.2609.32644","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.32644","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.32644","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.32644","pdf_url":"https://arxiv.org/pdf/2609.32644","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G3521806024","display_name":null,"funder_award_id":"12274228","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5522325295","display_name":"Theory and multiscale modelling","funder_award_id":"ANR-22-EXSP-0009","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G8572803201","display_name":"Science et Ing\u00e9nierie \u00e0 l'Echelle Nano","funder_award_id":"ANR-17-EURE-0009","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214726658.pdf","grobid_xml":"https://content.openalex.org/works/W7214726658.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7166856055"],"related_works":["https://openalex.org/W4385016878","https://openalex.org/W2002014494","https://openalex.org/W1984815921","https://openalex.org/W2022601594","https://openalex.org/W1998530696","https://openalex.org/W2071580937","https://openalex.org/W1993228889","https://openalex.org/W7034171175","https://openalex.org/W2037547623","https://openalex.org/W2084870458"],"abstract_inverted_index":{"Recent":[0],"advances":[1],"in":[2,28,71,89,121,141,167,209],"intrinsic":[3],"two-dimensional":[4],"(2D)":[5],"magnets":[6],"have":[7],"created":[8],"a":[9,12,117],"need":[10],"for":[11],"unified":[13],"understanding":[14],"of":[15,58,135,150],"finite-temperature":[16,26],"phase":[17],"transitions":[18],"across":[19],"different":[20],"spin-symmetry":[21],"classes.":[22],"Here,":[23],"we":[24,93,160],"investigate":[25],"magnetism":[27],"the":[29,41,56,72,80,90,96,102,122,133,139,148,151,163,173,181],"classical":[30],"2D":[31,211],"Heisenberg":[32,74,170],"model":[33],"using":[34],"large-scale":[35],"Monte":[36],"Carlo":[37],"simulations,":[38],"continuously":[39],"spanning":[40],"easy-plane,":[42],"isotropic,":[43],"and":[44,61,76,82,104,158,187,195,206],"easy-axis":[45,83],"regimes.":[46],"We":[47,124],"find":[48,94],"that":[49,95,126,162],"characteristic":[50,97,127,165],"temperatures":[51,98,128],"are":[52,130],"strongly":[53],"affected":[54],"by":[55,65,112,143],"interplay":[57,182],"finite-size":[59,184],"effects":[60],"spin":[62,185,204],"symmetry,":[63,205],"induced":[64],"magnetocrystalline":[66],"anisotropy,":[67,203],"being":[68],"most":[69],"pronounced":[70],"isotropic":[73],"regime":[75],"substantially":[77],"reduced":[78],"toward":[79],"easy-plane":[81,91,169],"limits.":[84],"Examining":[85],"Berezinskii--Kosterlitz--Thouless":[86],"(BKT)":[87],"physics":[88],"regime,":[92],"independently":[99],"estimated":[100],"from":[101,109,175],"magnetization":[103],"heat":[105],"capacity":[106],"deviate":[107],"significantly":[108],"those":[110],"proposed":[111],"BKT":[113,176],"theory,":[114,177],"but":[115],"match":[116],"previously":[118],"reported":[119],"anomaly":[120],"XY-model.":[123],"report":[125],"instead":[129],"correlated":[131],"with":[132,201],"proliferation":[134],"vortex-antivortex":[136],"pairs,":[137],"suggesting":[138],"gain":[140],"entropy":[142],"their":[144],"accelerated":[145],"nucleation":[146],"as":[147],"origin":[149],"anomaly.":[152],"Establishing":[153],"this":[154],"connection":[155],"both":[156],"theoretically":[157],"numerically,":[159],"argue":[161],"thermodynamic":[164],"temperature":[166,198],"finite":[168,210],"magnets,":[171],"including":[172],"deviation":[174],"is":[178],"subject":[179],"to":[180],"between":[183],"correlations":[186],"vortex":[188],"proliferation.":[189],"These":[190],"results":[191],"clarify":[192],"how":[193],"experimental":[194],"technologically":[196],"relevant":[197],"scales":[199],"evolve":[200],"magnetic":[202],"system":[207],"size":[208],"magnets.":[212]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-30T00:00:00"}