{"id":"https://openalex.org/W7203727121","doi":"https://doi.org/10.48550/arxiv.2608.16557","title":"Absence of critical scaling in the Schelling segregation model","display_name":"Absence of critical scaling in the Schelling segregation model","publication_year":2026,"publication_date":"2026-08-17","ids":{"openalex":"https://openalex.org/W7203727121","doi":"https://doi.org/10.48550/arxiv.2608.16557"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.16557","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.16557","pdf_url":"https://arxiv.org/pdf/2608.16557","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/2608.16557","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5147439155","display_name":"Sam Rifaki","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Rifaki, Mouhssine","raw_affiliation_strings":["Stanford University , Stanford , CA 94305 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Stanford University , Stanford , CA 94305 , USA","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5147439155"],"corresponding_institution_ids":["https://openalex.org/I97018004"],"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":0.6420999765396118,"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":0.6420999765396118,"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/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.2687999904155731,"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/T12162","display_name":"Cellular Automata and Applications","score":0.006599999964237213,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/schelling-segregation-model","display_name":"Schelling segregation model","score":0.9950000047683716},{"id":"https://openalex.org/keywords/critical-scaling","display_name":"critical scaling","score":0.6510000228881836},{"id":"https://openalex.org/keywords/finite-size-scaling","display_name":"finite-size scaling","score":0.8090000152587891},{"id":"https://openalex.org/keywords/moore-neighborhood","display_name":"Moore neighborhood","score":0.871999979019165},{"id":"https://openalex.org/keywords/binder-cumulant","display_name":"Binder cumulant","score":0.8500000238418579},{"id":"https://openalex.org/keywords/critical-exponents","display_name":"critical exponents","score":0.722000002861023},{"id":"https://openalex.org/keywords/beta-distribution","display_name":"beta distribution","score":0.5910000205039978},{"id":"https://openalex.org/keywords/long-range-correlations","display_name":"long-range correlations","score":0.6700000166893005},{"id":"https://openalex.org/keywords/phase-transitions","display_name":"phase transitions","score":0.5669999718666077},{"id":"https://openalex.org/keywords/social-segregation","display_name":"social segregation","score":0.4020000100135803}],"concepts":[{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.878600001335144},{"id":"https://openalex.org/C51329190","wikidata":"https://www.wikidata.org/wiki/Q1076349","display_name":"Ising model","level":2,"score":0.6614999771118164},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5932000279426575},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.588699996471405},{"id":"https://openalex.org/C196298200","wikidata":"https://www.wikidata.org/wiki/Q577705","display_name":"Critical point (mathematics)","level":2,"score":0.513700008392334},{"id":"https://openalex.org/C125611927","wikidata":"https://www.wikidata.org/wiki/Q17008131","display_name":"Criticality","level":2,"score":0.5076000094413757},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.46160000562667847},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.4496000111103058},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.3379000127315521},{"id":"https://openalex.org/C177407944","wikidata":"https://www.wikidata.org/wiki/Q7998780","display_name":"Widom scaling","level":4,"score":0.33719998598098755},{"id":"https://openalex.org/C194807282","wikidata":"https://www.wikidata.org/wiki/Q900634","display_name":"Critical phenomena","level":3,"score":0.3292999863624573},{"id":"https://openalex.org/C2780388094","wikidata":"https://www.wikidata.org/wiki/Q1666248","display_name":"Intermittency","level":3,"score":0.3154999911785126},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.30869999527931213},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.30660000443458557},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.30559998750686646},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.2890999913215637},{"id":"https://openalex.org/C43711488","wikidata":"https://www.wikidata.org/wiki/Q7534783","display_name":"Skew","level":2,"score":0.2815999984741211},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27900001406669617},{"id":"https://openalex.org/C112675119","wikidata":"https://www.wikidata.org/wiki/Q2992284","display_name":"Periodic boundary conditions","level":3,"score":0.2705000042915344},{"id":"https://openalex.org/C135593079","wikidata":"https://www.wikidata.org/wiki/Q1750766","display_name":"Scale invariance","level":2,"score":0.2632000148296356},{"id":"https://openalex.org/C174256460","wikidata":"https://www.wikidata.org/wiki/Q911364","display_name":"Perturbation theory (quantum mechanics)","level":2,"score":0.2538999915122986}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.16557","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.16557","pdf_url":"https://arxiv.org/pdf/2608.16557","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.2608.16557","doi":"https://doi.org/10.48550/arxiv.2608.16557","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.16557","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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.16557","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.16557","pdf_url":"https://arxiv.org/pdf/2608.16557","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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7203727121.pdf","grobid_xml":"https://content.openalex.org/works/W7203727121.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1970999172","https://openalex.org/W1977578104","https://openalex.org/W2001629016","https://openalex.org/W2016454625","https://openalex.org/W2026665791","https://openalex.org/W2058105398","https://openalex.org/W2076922992","https://openalex.org/W2085642400","https://openalex.org/W2088336517","https://openalex.org/W2110988681","https://openalex.org/W2112848633","https://openalex.org/W2785542042"],"related_works":["https://openalex.org/W2054974645","https://openalex.org/W2790196799","https://openalex.org/W4297050838","https://openalex.org/W2618588625","https://openalex.org/W7015234439","https://openalex.org/W7097572114","https://openalex.org/W143374940","https://openalex.org/W7100132851","https://openalex.org/W2896562387","https://openalex.org/W2254038493"],"abstract_inverted_index":{"We":[0],"find":[1],"no":[2,170],"evidence":[3,118],"of":[4,129,217],"critical":[5,196,259],"scaling":[6,51,76,117],"in":[7,12,53,220],"the":[8,14,54,58,75,112,116,142,149,155,166,174,195,215,227,235,254],"Schelling":[9,255],"segregation":[10,239],"model,":[11],"either":[13],"Moore":[15,55,85],"neighborhood":[16,86],"or":[17],"its":[18],"dense-spectrum":[19,152],"extension":[20,153],"to":[21,25,37,89,139,187],"Chebyshev":[22],"radii":[23],"up":[24,36],"$r_0":[26,159,183],"=":[27,30,39,184,189],"6$":[28],"($k":[29],"168$":[31],"neighbors).":[32],"On":[33],"periodic":[34],"grids":[35],"$L":[38,163,188,209],"320$":[40,190],"with":[41,92,101],"50":[42],"trials":[43],"per":[44],"point":[45],"(>":[46],"12,500":[47],"runs),":[48],"every":[49],"finite-size":[50],"diagnostic":[52],"baseline":[56],"fails:":[57],"per-$L$":[59,175],"$T_c$":[60,176],"does":[61,107],"not":[62,108,226],"drift,":[63],"Var$(S)":[64],"\\sim":[65],"L^{-2.02":[66],"\\pm":[67],"0.09}$":[68],"matches":[69],"trivial":[70],"averaging,":[71],"$\u03b3/\u03bd\\approx":[72],"0$,":[73],"and":[74,133,173,180,248],"collapse":[77],"never":[78],"reaches":[79],"a":[80,98,231],"finite":[81,147],"optimum.":[82],"The":[83,151,212,245],"8-site":[84],"restricts":[87],"satisfaction":[88],"ratios":[90],"$j/k$":[91],"$k":[93],"\\leq":[94],"8$,":[95],"giving":[96],"$S(T)$":[97],"staircase":[99,228,246],"structure":[100],"23":[102],"rational":[103],"thresholds;":[104],"discreteness":[105],"alone":[106],"forbid":[109],"criticality":[110],"(cf.":[111],"Ising":[113],"model),":[114],"but":[115],"rules":[119],"it":[120],"out":[121],"empirically.":[122],"A":[123],"branching-ratio":[124],"calculation":[125],"predicts":[126],"subcritical":[127],"cascades":[128],"mean":[130],"size":[131],"$1/(1-R)$":[132],"is":[134,178,214],"validated":[135],"by":[136],"perturbation":[137],"experiments":[138],"within":[140],"15%;":[141],"multiscalar":[143],"dissimilarity":[144],"length":[145],"stays":[146],"across":[148,158],"transition.":[150],"strengthens":[154],"negative":[156],"verdict:":[157],"\\in":[160,164,210],"{3,4,5,6}$":[161],"on":[162,208],"{40,80,160}$":[165],"Binder":[167],"cumulant":[168],"has":[169],"$L$-curve":[171],"crossing":[172],"drift":[177],"monotonic":[179],"unsaturated;":[181],"at":[182,241],"4$,":[185],"extending":[186],"gives":[191],"$\u03b1=":[192,198,203],"-2.70$,":[193],"below":[194],"boundary":[197],"-2$,":[199],"dissolving":[200],"an":[201],"apparent":[202],"+0.81$":[204],"signal":[205],"visible":[206],"only":[207],"{40,80}$.":[211],"mechanism":[213,250],"absence":[216],"long-range":[218],"correlation":[219],"equilibrium":[221],"plus":[222],"deterministic":[223],"high-$k$":[224],"dynamics,":[225],"structure.":[229],"With":[230],"Beta-distributed":[232],"heterogeneous":[233],"tolerance,":[234],"intolerant":[236],"tail":[237],"drives":[238],"even":[240],"moderate":[242],"population-average":[243],"tolerance.":[244],"theorem":[247],"cascade":[249],"together":[251],"account":[252],"for":[253],"transition":[256],"without":[257],"invoking":[258],"phenomena.":[260]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-08-19T00:00:00"}
