{"id":"https://openalex.org/W2988930280","doi":"https://doi.org/10.48550/arxiv.1911.00032","title":"Free Variable Loop Equations for the 3-State Potts Model Coupled to 2D Gravity","display_name":"Free Variable Loop Equations for the 3-State Potts Model Coupled to 2D Gravity","publication_year":2019,"publication_date":"2019-10-31","ids":{"openalex":"https://openalex.org/W2988930280","doi":"https://doi.org/10.48550/arxiv.1911.00032","mag":"2988930280"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:1911.00032","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1911.00032","pdf_url":"https://arxiv.org/pdf/1911.00032","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/1911.00032","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029725024","display_name":"Aravinth Kulanthaivelu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Kulanthaivelu, Aravinth","raw_affiliation_strings":["Rudolf Peierls Centre for Theoretical Physics , Clarendon Laboratory , Parks Road , University of Oxford , Oxford OX1 3PU , UK","University of Oxford"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Rudolf Peierls Centre for Theoretical Physics , Clarendon Laboratory , Parks Road , University of Oxford , Oxford OX1 3PU , UK","institution_ids":["https://openalex.org/I40120149"]},{"raw_affiliation_string":"University of Oxford","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5029725024"],"corresponding_institution_ids":["https://openalex.org/I40120149"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"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/T11716","display_name":"Random Matrices and Applications","score":0.7188000082969666,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.7188000082969666,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10025","display_name":"Black Holes and Theoretical Physics","score":0.1356000006198883,"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/T11415","display_name":"Noncommutative and Quantum Gravity Theories","score":0.039400000125169754,"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/three-state-potts-model","display_name":"three-state Potts model","score":0.9649999737739563},{"id":"https://openalex.org/keywords/matrix-models","display_name":"matrix models","score":0.6949999928474426},{"id":"https://openalex.org/keywords/generating-functions","display_name":"generating functions","score":0.6510000228881836},{"id":"https://openalex.org/keywords/disk-amplitudes","display_name":"disk amplitudes","score":0.9700000286102295},{"id":"https://openalex.org/keywords/spectral-curves","display_name":"spectral curves","score":0.8360000252723694},{"id":"https://openalex.org/keywords/planar-graphs","display_name":"planar graphs","score":0.8320000171661377}],"concepts":[{"id":"https://openalex.org/C98925819","wikidata":"https://www.wikidata.org/wiki/Q7235385","display_name":"Potts model","level":3,"score":0.7146021723747253},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.5971516370773315},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.592801034450531},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.4837951362133026},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.450168639421463},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.44361454248428345},{"id":"https://openalex.org/C129537906","wikidata":"https://www.wikidata.org/wiki/Q7603913","display_name":"State variable","level":2,"score":0.4265856444835663},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.42409729957580566},{"id":"https://openalex.org/C184670325","wikidata":"https://www.wikidata.org/wiki/Q512604","display_name":"Loop (graph theory)","level":2,"score":0.4217653274536133},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3805093765258789},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3227813243865967},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.18116018176078796},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.16690507531166077},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.16512256860733032},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15464845299720764},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14944079518318176},{"id":"https://openalex.org/C51329190","wikidata":"https://www.wikidata.org/wiki/Q1076349","display_name":"Ising model","level":2,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:1911.00032","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1911.00032","pdf_url":"https://arxiv.org/pdf/1911.00032","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.1911.00032","doi":"https://doi.org/10.48550/arxiv.1911.00032","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1911.00032","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:1911.00032","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1911.00032","pdf_url":"https://arxiv.org/pdf/1911.00032","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/G5696635624","display_name":"STFC Oxford Physics 2015 DTP","funder_award_id":"ST/N504233/1","funder_id":"https://openalex.org/F4320334632","funder_display_name":"Science and Technology Facilities Council"}],"funders":[{"id":"https://openalex.org/F4320334632","display_name":"Science and Technology Facilities Council","ror":"https://ror.org/057g20z61"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2988930280.pdf","grobid_xml":"https://content.openalex.org/works/W2988930280.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W1627601052"],"related_works":["https://openalex.org/W2046600193","https://openalex.org/W7214245951","https://openalex.org/W7099765224","https://openalex.org/W2091500150","https://openalex.org/W2062687046","https://openalex.org/W2110451032","https://openalex.org/W1627601052","https://openalex.org/W2033875802","https://openalex.org/W7098511460","https://openalex.org/W2171240654"],"abstract_inverted_index":{"We":[0],"revisit":[1],"the":[2,7,14,21,26,60,70,99,103],"long":[3],"standing":[4],"problem":[5],"of":[6,25,41,62,68,81,95],"geometric":[8],"free":[9],"variable":[10],"approach":[11],"to":[12,31,49],"computing":[13],"generating":[15,53,71,106],"function":[16],"for":[17,102],"disk":[18],"amplitudes":[19],"in":[20,55],"matrix":[22],"model":[23,29],"formulation":[24],"3-state":[27],"Potts":[28],"coupled":[30],"2D":[32],"discrete":[33],"gravity.":[34],"This":[35],"method":[36,67],"is":[37,73],"a":[38,51,78,92],"mild":[39],"generalisation":[40],"Schwinger":[42],"Dyson":[43],"(loop-)equations":[44],"approach,":[45],"using":[46],"graphical":[47],"arguments":[48],"derive":[50,91],"single":[52],"equation":[54,72],"non-commutative":[56],"variables":[57],"that":[58,97],"contain":[59],"information":[61],"all":[63],"loop":[64],"equations.":[65],"The":[66],"constructing":[69],"reviewed,":[74],"we":[75,90],"explain":[76],"how":[77],"larger":[79],"class":[80],"constraints":[82],"than":[83],"previously":[84],"known":[85],"can":[86],"be":[87],"constructed":[88],"and":[89],"closed":[93],"set":[94],"equations":[96],"determine":[98],"spectral":[100],"curve":[101],"planar":[104],"graph":[105],"function.":[107]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2019-11-22T00:00:00"}