{"id":"https://openalex.org/W7204877909","doi":"https://doi.org/10.48550/arxiv.2608.29090","title":"Detecting Multiple Phase Transitions in Lattice Systems with Intrinsic Dimensions","display_name":"Detecting Multiple Phase Transitions in Lattice Systems with Intrinsic Dimensions","publication_year":2026,"publication_date":"2026-08-29","ids":{"openalex":"https://openalex.org/W7204877909","doi":"https://doi.org/10.48550/arxiv.2608.29090"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.29090","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29090","pdf_url":"https://arxiv.org/pdf/2608.29090","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/2608.29090","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091526874","display_name":"Jie Mei","orcid":"https://orcid.org/0000-0001-9826-9291","observed_orcids":["https://orcid.org/0000-0001-9826-9291"]},"institutions":[{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mei, Jie","raw_affiliation_strings":["School of Nuclear Science and Technology , University of Chinese Academy of Sciences , Beijing , 100049 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Nuclear Science and Technology , University of Chinese Academy of Sciences , Beijing , 100049 , China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074770743","display_name":"Tetsuo Hatsuda","orcid":"https://orcid.org/0000-0003-2206-9810","observed_orcids":["https://orcid.org/0000-0003-2206-9810"]},"institutions":[{"id":"https://openalex.org/I166644833","display_name":"Kavli Institute for the Physics and Mathematics of the Universe","ror":"https://ror.org/02chw6z69","country_code":"JP","type":"facility","lineage":["https://openalex.org/I166644833","https://openalex.org/I4405286593","https://openalex.org/I74801974"]},{"id":"https://openalex.org/I4405259317","display_name":"RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences","ror":"https://ror.org/022hvg611","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210110652","https://openalex.org/I4405259317"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hatsuda, Tetsuo","raw_affiliation_strings":["Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU) ,","RIKEN Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS) , Wako , Saitama 351-0198 , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU) ,","institution_ids":["https://openalex.org/I166644833"]},{"raw_affiliation_string":"RIKEN Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS) , Wako , Saitama 351-0198 , Japan","institution_ids":["https://openalex.org/I4405259317"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125228608","display_name":"Mei Huang","orcid":"https://orcid.org/0000-0002-3451-2501","observed_orcids":["https://orcid.org/0000-0002-3451-2501"]},"institutions":[{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]},{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["CN","JP"],"is_corresponding":false,"raw_author_name":"Huang, Mei","raw_affiliation_strings":["School of Nuclear Science and Technology , University of Chinese Academy of Sciences , Beijing , 100049 , China","WPI , The University of Tokyo , Kashiwa , 277-8568 , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Nuclear Science and Technology , University of Chinese Academy of Sciences , Beijing , 100049 , China","institution_ids":["https://openalex.org/I4210165038"]},{"raw_affiliation_string":"WPI , The University of Tokyo , Kashiwa , 277-8568 , Japan","institution_ids":["https://openalex.org/I74801974"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5148883893","display_name":"Lingxiao Wang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4405259317","display_name":"RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences","ror":"https://ror.org/022hvg611","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210110652","https://openalex.org/I4405259317"]},{"id":"https://openalex.org/I4405287287","display_name":"Institute for Physics of Intelligence","ror":"https://ror.org/04qartm12","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4405287287","https://openalex.org/I74801974"]},{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Wang, Lingxiao","raw_affiliation_strings":["Institute for Physics of Intelligence , The University of Tokyo , Hongo , Tokyo 113-0033 , Japan","RIKEN Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS) , Wako , Saitama 351-0198 , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Physics of Intelligence , The University of Tokyo , Hongo , Tokyo 113-0033 , Japan","institution_ids":["https://openalex.org/I4405287287","https://openalex.org/I74801974"]},{"raw_affiliation_string":"RIKEN Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS) , Wako , Saitama 351-0198 , Japan","institution_ids":["https://openalex.org/I4405259317"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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":0.9423999786376953,"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":0.9423999786376953,"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/T10224","display_name":"Quantum Chromodynamics and Particle Interactions","score":0.02250000089406967,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy 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/T10527","display_name":"High-Energy Particle Collisions Research","score":0.011300000362098217,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy 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/intrinsic-dimension","display_name":"intrinsic dimension","score":0.8109999895095825},{"id":"https://openalex.org/keywords/multiple-phase-transitions","display_name":"multiple phase transitions","score":0.8790000081062317},{"id":"https://openalex.org/keywords/lattice-systems","display_name":"lattice systems","score":0.7770000100135803},{"id":"https://openalex.org/keywords/clock-model","display_name":"clock model","score":0.8190000057220459},{"id":"https://openalex.org/keywords/berezinskii-kosterlitz-thouless-transition","display_name":"Kosterlitz-Thouless transition","score":0.9879999756813049},{"id":"https://openalex.org/keywords/u-1-higgs-model","display_name":"U(1) Higgs model","score":0.8840000033378601},{"id":"https://openalex.org/keywords/gauge-redundancy","display_name":"gauge redundancy","score":0.6159999966621399},{"id":"https://openalex.org/keywords/configuration-space-geometry","display_name":"configuration space geometry","score":0.7639999985694885},{"id":"https://openalex.org/keywords/deconfinement","display_name":"deconfinement","score":0.7860000133514404},{"id":"https://openalex.org/keywords/chiral-crossover","display_name":"chiral crossover","score":0.9739999771118164}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.7102000117301941},{"id":"https://openalex.org/C122507166","wikidata":"https://www.wikidata.org/wiki/Q628906","display_name":"Crossover","level":2,"score":0.5788000226020813},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.574400007724762},{"id":"https://openalex.org/C149288129","wikidata":"https://www.wikidata.org/wiki/Q185357","display_name":"Phase transition","level":2,"score":0.5723999738693237},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5421000123023987},{"id":"https://openalex.org/C51329190","wikidata":"https://www.wikidata.org/wiki/Q1076349","display_name":"Ising model","level":2,"score":0.4523000121116638},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.44369998574256897},{"id":"https://openalex.org/C158129726","wikidata":"https://www.wikidata.org/wiki/Q402","display_name":"Higgs boson","level":2,"score":0.42500001192092896},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.4205999970436096},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.41119998693466187},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.39989998936653137},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.3601999878883362},{"id":"https://openalex.org/C17269025","wikidata":"https://www.wikidata.org/wiki/Q3283","display_name":"Geometric phase","level":2,"score":0.3458000123500824},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2944999933242798},{"id":"https://openalex.org/C181830111","wikidata":"https://www.wikidata.org/wiki/Q214850","display_name":"Gauge theory","level":2,"score":0.28859999775886536},{"id":"https://openalex.org/C32546565","wikidata":"https://www.wikidata.org/wiki/Q856711","display_name":"Magnetization","level":3,"score":0.2883000075817108},{"id":"https://openalex.org/C194807282","wikidata":"https://www.wikidata.org/wiki/Q900634","display_name":"Critical phenomena","level":3,"score":0.2791000008583069},{"id":"https://openalex.org/C152124472","wikidata":"https://www.wikidata.org/wiki/Q1204361","display_name":"Redundancy (engineering)","level":2,"score":0.27880001068115234},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.271699994802475},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.266400009393692}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.29090","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29090","pdf_url":"https://arxiv.org/pdf/2608.29090","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.29090","doi":"https://doi.org/10.48550/arxiv.2608.29090","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.29090","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.29090","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29090","pdf_url":"https://arxiv.org/pdf/2608.29090","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204877909.pdf","grobid_xml":"https://content.openalex.org/works/W7204877909.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W1554227327","https://openalex.org/W1715636977","https://openalex.org/W1959608418","https://openalex.org/W1970505387","https://openalex.org/W2022890198","https://openalex.org/W2073511410","https://openalex.org/W2101512932","https://openalex.org/W2127170466","https://openalex.org/W2146553833","https://openalex.org/W2337082154","https://openalex.org/W2531147647","https://openalex.org/W2754478492","https://openalex.org/W2795371312","https://openalex.org/W2905459524","https://openalex.org/W2909292814","https://openalex.org/W2946857231","https://openalex.org/W2997125714","https://openalex.org/W3005146677","https://openalex.org/W3036035706","https://openalex.org/W3135134815","https://openalex.org/W4221140744","https://openalex.org/W4315881573","https://openalex.org/W4319347025","https://openalex.org/W4321111739","https://openalex.org/W4388736459","https://openalex.org/W4389728521","https://openalex.org/W4404041489","https://openalex.org/W4406081012","https://openalex.org/W4410495118","https://openalex.org/W7157049673","https://openalex.org/W7163656446"],"related_works":["https://openalex.org/W2002914072","https://openalex.org/W3036035706","https://openalex.org/W163798379","https://openalex.org/W2028024244","https://openalex.org/W1995950240","https://openalex.org/W1999466028","https://openalex.org/W7163081588","https://openalex.org/W7163868772","https://openalex.org/W2074574735","https://openalex.org/W1973951641"],"abstract_inverted_index":{"Lattice":[0],"systems":[1,179],"with":[2,22,126,180],"multiple":[3,181],"nearby":[4],"transitions":[5,124,182],"pose":[6],"two":[7,97],"related":[8],"challenges:":[9],"resolving":[10],"distinct":[11],"transition":[12],"scales":[13,193],"and":[14,61,68,90,114,183,190],"identifying":[15],"the":[16,28,38,49,54,58,75,78,96,100,127,133,157],"degrees":[17,129],"of":[18,31,120,130,138,159,177],"freedom":[19],"primarily":[20],"associated":[21,125],"each":[23,121],"transition.":[24],"We":[25,140],"show":[26,142],"that":[27,143],"intrinsic":[29,55,108,144,171],"dimension":[30,56,172],"Monte":[32],"Carlo":[33],"configuration":[34],"ensembles,":[35],"estimated":[36],"by":[37,153],"two-nearest-neighbors":[39],"method,":[40],"provides":[41],"a":[42,83,174],"geometric":[43,175],"diagnostic":[44],"for":[45,64],"both":[46,65],"problems.":[47],"In":[48,74,99],"two-dimensional":[50],"$q$-state":[51],"clock":[52],"model,":[53,104],"distinguishes":[57],"ordered,":[59],"quasi-critical,":[60],"disordered":[62],"regimes":[63],"well-separated":[66],"($q=9$)":[67],"closely":[69],"spaced":[70],"($q=5$)":[71],"Berezinskii--Kosterlitz--Thouless":[72],"transitions.":[73,98],"$q=5$":[76],"case,":[77],"intermediate":[79],"phase":[80],"appears":[81],"as":[82,173],"broad":[84],"low-dimensional":[85],"valley":[86],"even":[87],"when":[88],"energy":[89],"magnetization":[91],"do":[92],"not":[93],"separately":[94],"resolve":[95],"four-dimensional":[101],"$U(1)$":[102],"Higgs":[103,115],"we":[105],"introduce":[106],"channel-decomposed":[107,170],"dimensions":[109,145],"based":[110],"on":[111,148],"gauge-invariant":[112],"plaquette":[113],"variables.":[116],"The":[117],"dominant":[118],"response":[119],"channel":[122,135],"tracks":[123],"corresponding":[128],"freedom,":[131],"while":[132],"combined":[134],"retains":[136],"features":[137],"both.":[139],"further":[141],"evaluated":[146],"directly":[147],"gauge-variant":[149],"fields":[150],"are":[151],"dominated":[152],"gauge-orbit":[154],"directions,":[155],"demonstrating":[156],"importance":[158],"removing":[160],"gauge":[161],"redundancy":[162],"before":[163],"interpreting":[164],"configuration-space":[165],"geometry.":[166],"These":[167],"results":[168],"establish":[169],"probe":[176],"lattice":[178],"motivate":[184],"its":[185],"application":[186],"to":[187],"disentangling":[188],"deconfinement":[189],"chiral":[191],"crossover":[192],"in":[194],"full":[195],"QCD.":[196]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-02T00:00:00"}