{"id":"https://openalex.org/W2022011815","doi":"https://doi.org/10.1103/physreve.85.066117","title":"Fragmentation transitions in multistate voter models","display_name":"Fragmentation transitions in multistate voter models","publication_year":2012,"publication_date":"2012-06-15","ids":{"openalex":"https://openalex.org/W2022011815","doi":"https://doi.org/10.1103/physreve.85.066117","mag":"2022011815","pmid":"https://pubmed.ncbi.nlm.nih.gov/23005172"},"language":"en","primary_location":{"id":"doi:10.1103/physreve.85.066117","doi":"https://doi.org/10.1103/physreve.85.066117","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physreve.85.066117","pdf_url":null,"source":{"id":"https://openalex.org/S35412551","display_name":"Physical Review E","issn_l":"1539-3755","issn":["1539-3755","1550-2376"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","vabb-shw"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review E","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1201.5198","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073274172","display_name":"Gesa A. B\u00f6hme","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I149899117","display_name":"Max Planck Society","ror":"https://ror.org/01hhn8329","country_code":"DE","type":"nonprofit","lineage":["https://openalex.org/I149899117"]},{"id":"https://openalex.org/I4210111875","display_name":"Max Planck Institute for the Physics of Complex Systems","ror":"https://ror.org/01bf9rw71","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210111875"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Gesa A. B\u00f6hme","raw_affiliation_strings":["Max-Planck Institute for the Physics of Complex Systems, Dresden, Germany. gesa@pks.mpg.de","Max Planck Institute for the Physics of Complex Systems, Max Planck Society"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Max-Planck Institute for the Physics of Complex Systems, Dresden, Germany. gesa@pks.mpg.de","institution_ids":["https://openalex.org/I4210111875"]},{"raw_affiliation_string":"Max Planck Institute for the Physics of Complex Systems, Max Planck Society","institution_ids":["https://openalex.org/I149899117","https://openalex.org/I4210111875"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076436751","display_name":"Thilo Gro\u00df","orcid":"https://orcid.org/0000-0002-1356-6690","observed_orcids":["https://orcid.org/0000-0002-1356-6690"]},"institutions":[{"id":"https://openalex.org/I4210111875","display_name":"Max Planck Institute for the Physics of Complex Systems","ror":"https://ror.org/01bf9rw71","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210111875"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Thilo Gross","raw_affiliation_strings":["Max-Planck Institute for the Physics of Complex Systems, Dresden, Germany","Department of Engineering Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Max-Planck Institute for the Physics of Complex Systems, Dresden, Germany","institution_ids":["https://openalex.org/I4210111875"]},{"raw_affiliation_string":"Department of Engineering Mathematics","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.5539,"has_fulltext":false,"cited_by_count":34,"citation_normalized_percentile":{"value":0.95020262,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"85","issue":"6","first_page":"066117","last_page":"066117"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":1.0,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear 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/T12592","display_name":"Opinion Dynamics and Social Influence","score":1.0,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear 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/T10064","display_name":"Complex Network Analysis Techniques","score":0.0,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear 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/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/opinion-formation","display_name":"opinion formation","score":0.9490000009536743},{"id":"https://openalex.org/keywords/social-networks","display_name":"social networks","score":0.7200000286102295},{"id":"https://openalex.org/keywords/opinion-dynamics","display_name":"opinion dynamics","score":0.46399998664855957},{"id":"https://openalex.org/keywords/phase-transitions","display_name":"phase transitions","score":0.38999998569488525},{"id":"https://openalex.org/keywords/agent-based-modeling","display_name":"agent-based modeling","score":0.5460000038146973},{"id":"https://openalex.org/keywords/analytical-results","display_name":"analytical results","score":0.35499998927116394}],"concepts":[{"id":"https://openalex.org/C2781396049","wikidata":"https://www.wikidata.org/wiki/Q7942158","display_name":"Voter model","level":2,"score":0.8832501173019409},{"id":"https://openalex.org/C191015642","wikidata":"https://www.wikidata.org/wiki/Q1132459","display_name":"Fragmentation (computing)","level":2,"score":0.875115156173706},{"id":"https://openalex.org/C158245278","wikidata":"https://www.wikidata.org/wiki/Q4386982","display_name":"Equidistant","level":2,"score":0.870495080947876},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.4809128940105438},{"id":"https://openalex.org/C194232998","wikidata":"https://www.wikidata.org/wiki/Q1606712","display_name":"Transition (genetics)","level":3,"score":0.4797162413597107},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4763334393501282},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.42954644560813904},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.24950066208839417},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24904966354370117},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.23690497875213623},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.11978563666343689},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06776097416877747},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003657","descriptor_name":"Decision Making","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003657","descriptor_name":"Decision Making","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003657","descriptor_name":"Decision Making","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008962","descriptor_name":"Models, Theoretical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008962","descriptor_name":"Models, Theoretical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008962","descriptor_name":"Models, Theoretical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D011639","descriptor_name":"Public Opinion","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D011639","descriptor_name":"Public Opinion","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D011639","descriptor_name":"Public Opinion","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D012919","descriptor_name":"Social Behavior","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D012919","descriptor_name":"Social Behavior","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D012919","descriptor_name":"Social Behavior","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":6,"locations":[{"id":"doi:10.1103/physreve.85.066117","doi":"https://doi.org/10.1103/physreve.85.066117","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physreve.85.066117","pdf_url":null,"source":{"id":"https://openalex.org/S35412551","display_name":"Physical Review E","issn_l":"1539-3755","issn":["1539-3755","1550-2376"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","vabb-shw"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review E","raw_type":"journal-article"},{"id":"pmid:23005172","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/23005172","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical review. E, Statistical, nonlinear, and soft matter physics","raw_type":"Journal Article"},{"id":"pmh:oai:arXiv.org:1201.5198","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1201.5198","pdf_url":"https://arxiv.org/pdf/1201.5198","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":"pmh:oai:pure.mpg.de:item_2219577","doi":null,"is_oa":false,"landing_page_url":"https://hdl.handle.net/11858/00-001M-0000-0029-89C1-C","pdf_url":null,"source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Physical Review E","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:research-information.bris.ac.uk:openaire_cris_publications/0e3bf3ac-c271-4643-91eb-3e9d66e18a89","doi":null,"is_oa":false,"landing_page_url":"https://hdl.handle.net/1983/0e3bf3ac-c271-4643-91eb-3e9d66e18a89","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"B\u00f6hme, G & Gross, T 2012, 'Fragmentation transitions in multi-state voter models', Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, vol. 85, 066117. https://doi.org/10.1103/PhysRevE.85.066117","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1201.5198","doi":"https://doi.org/10.48550/arxiv.1201.5198","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1201.5198","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1201.5198","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1201.5198","pdf_url":"https://arxiv.org/pdf/1201.5198","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":[],"sustainable_development_goals_aurora":[{"display_name":"Peace, justice, and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.7599999904632568}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W327553756","https://openalex.org/W1901962492","https://openalex.org/W1991442303","https://openalex.org/W1992015378","https://openalex.org/W1996250136","https://openalex.org/W1997976912","https://openalex.org/W2023544803","https://openalex.org/W2024433234","https://openalex.org/W2025827784","https://openalex.org/W2026968887","https://openalex.org/W2040467035","https://openalex.org/W2048297935","https://openalex.org/W2058871140","https://openalex.org/W2059848633","https://openalex.org/W2067613843","https://openalex.org/W2069033904","https://openalex.org/W2070722739","https://openalex.org/W2087622110","https://openalex.org/W2095395460","https://openalex.org/W2104915249","https://openalex.org/W2121239718","https://openalex.org/W2124637492","https://openalex.org/W2127242730","https://openalex.org/W2131767739","https://openalex.org/W2146008209","https://openalex.org/W2148606196","https://openalex.org/W2158815557","https://openalex.org/W3104398963","https://openalex.org/W4206651839"],"related_works":["https://openalex.org/W2055230676","https://openalex.org/W2373708349","https://openalex.org/W2370379095","https://openalex.org/W2064284991","https://openalex.org/W2385837322","https://openalex.org/W2546071705","https://openalex.org/W2354382931","https://openalex.org/W2123581415","https://openalex.org/W2392576975","https://openalex.org/W2378019422"],"abstract_inverted_index":{"Adaptive":[0],"models":[1,29,79],"of":[2,28,33,82],"opinion":[3],"formation":[4],"among":[5],"humans":[6],"can":[7,84],"display":[8],"a":[9,13,26,51,64],"fragmentation":[10,90],"transition,":[11],"where":[12],"social":[14],"network":[15],"breaks":[16],"into":[17],"disconnected":[18],"components.":[19],"Here":[20],"we":[21,40,74],"investigate":[22],"this":[23],"transition":[24],"in":[25,63,77],"class":[27],"with":[30],"arbitrary":[31],"number":[32,81],"opinions.":[34],"In":[35],"contrast":[36],"to":[37],"previous":[38],"work":[39],"do":[41],"not":[42],"assume":[43],"that":[44,76],"opinions":[45,83],"are":[46,68],"equidistant":[47],"or":[48],"arranged":[49],"on":[50,61],"one-dimensional":[52],"conceptual":[53],"axis.":[54],"Our":[55],"investigation":[56],"reveals":[57],"detailed":[58],"analytical":[59],"results":[60],"fragmentations":[62],"three-opinion":[65],"model,":[66],"which":[67],"confirmed":[69],"by":[70],"agent-based":[71],"simulations.":[72],"Furthermore,":[73],"show":[75],"certain":[78],"the":[80,89],"be":[85],"reduced":[86],"without":[87],"affecting":[88],"points.":[91]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":1}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2025-10-10T00:00:00"}