{"id":"https://openalex.org/W7213601622","doi":"https://doi.org/10.48550/arxiv.2609.20210","title":"Learning the Emergent Bulk Geometry of the Three Dimensional Ising Model","display_name":"Learning the Emergent Bulk Geometry of the Three Dimensional Ising Model","publication_year":2026,"publication_date":"2026-07-25","ids":{"openalex":"https://openalex.org/W7213601622","doi":"https://doi.org/10.48550/arxiv.2609.20210"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.20210","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20210","pdf_url":"https://arxiv.org/pdf/2609.20210","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/2609.20210","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068165646","display_name":"Ritam Basu","orcid":"https://orcid.org/0009-0005-6281-9390","observed_orcids":["https://orcid.org/0009-0005-6281-9390"]},"institutions":[{"id":"https://openalex.org/I11947397","display_name":"Tata Institute of Fundamental Research","ror":"https://ror.org/03ht1xw27","country_code":"IN","type":"education","lineage":["https://openalex.org/I11947397","https://openalex.org/I2799351866","https://openalex.org/I3149292468"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Basu, Ritam","raw_affiliation_strings":["Department of Theoretical Physics , Tata Institute of Fundamental Research , 1 Homi Bhabha Road , Mumbai 400005 , India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Theoretical Physics , Tata Institute of Fundamental Research , 1 Homi Bhabha Road , Mumbai 400005 , India","institution_ids":["https://openalex.org/I11947397"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5068165646"],"corresponding_institution_ids":["https://openalex.org/I11947397"],"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/T10025","display_name":"Black Holes and Theoretical Physics","score":0.9761000275611877,"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"}},"topics":[{"id":"https://openalex.org/T10025","display_name":"Black Holes and Theoretical Physics","score":0.9761000275611877,"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":0.002099999925121665,"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/T10224","display_name":"Quantum Chromodynamics and Particle Interactions","score":0.0015999999595806003,"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/3d-ising-model","display_name":"three-dimensional Ising model","score":0.9419999718666077},{"id":"https://openalex.org/keywords/ads-cft-correspondence","display_name":"AdS/CFT correspondence","score":0.8939999938011169},{"id":"https://openalex.org/keywords/differentiable-solvers","display_name":"differentiable solvers","score":0.6069999933242798},{"id":"https://openalex.org/keywords/probe-field","display_name":"probe field","score":0.718999981880188},{"id":"https://openalex.org/keywords/boundary-operators","display_name":"boundary operators","score":0.5619999766349792},{"id":"https://openalex.org/keywords/central-charge","display_name":"central charge","score":0.6690000295639038},{"id":"https://openalex.org/keywords/metric-reconstruction","display_name":"metric reconstruction","score":0.42399999499320984},{"id":"https://openalex.org/keywords/machine-learning","display_name":"machine learning","score":0.35499998927116394}],"concepts":[{"id":"https://openalex.org/C51329190","wikidata":"https://www.wikidata.org/wiki/Q1076349","display_name":"Ising model","level":2,"score":0.8507999777793884},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5601000189781189},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.5450000166893005},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.526199996471405},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.515500009059906},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.4957999885082245},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.48350000381469727},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.48080000281333923},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4262999892234802},{"id":"https://openalex.org/C60718061","wikidata":"https://www.wikidata.org/wiki/Q1414747","display_name":"Momentum (technical analysis)","level":2,"score":0.3840999901294708},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.3831000030040741},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.3634999990463257},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.3467000126838684},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.31679999828338623},{"id":"https://openalex.org/C158843486","wikidata":"https://www.wikidata.org/wiki/Q2137810","display_name":"Complex geometry","level":2,"score":0.3070000112056732},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3001999855041504},{"id":"https://openalex.org/C194807282","wikidata":"https://www.wikidata.org/wiki/Q900634","display_name":"Critical phenomena","level":3,"score":0.29490000009536743},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.2919999957084656},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.25859999656677246},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.2524000108242035}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.20210","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20210","pdf_url":"https://arxiv.org/pdf/2609.20210","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.2609.20210","doi":"https://doi.org/10.48550/arxiv.2609.20210","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.20210","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:2609.20210","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20210","pdf_url":"https://arxiv.org/pdf/2609.20210","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213601622.pdf","grobid_xml":"https://content.openalex.org/works/W7213601622.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1889142700","https://openalex.org/W1965475689","https://openalex.org/W1969758109","https://openalex.org/W2005927412","https://openalex.org/W2039609754","https://openalex.org/W2121583605","https://openalex.org/W2128233898","https://openalex.org/W2143468696","https://openalex.org/W2166248051","https://openalex.org/W2245814237","https://openalex.org/W2561233827","https://openalex.org/W2625696144","https://openalex.org/W2788808196","https://openalex.org/W2808746463","https://openalex.org/W2892666903","https://openalex.org/W2970971581","https://openalex.org/W3010983423","https://openalex.org/W3035965352","https://openalex.org/W3127566303","https://openalex.org/W4353092629","https://openalex.org/W4393227626","https://openalex.org/W4406980228","https://openalex.org/W4408756470","https://openalex.org/W4417267784"],"related_works":["https://openalex.org/W4415191738","https://openalex.org/W6941570793","https://openalex.org/W2158637191","https://openalex.org/W2788808196","https://openalex.org/W2129781078","https://openalex.org/W2848267807","https://openalex.org/W4406119884","https://openalex.org/W2034208461","https://openalex.org/W3038443050","https://openalex.org/W7213505604"],"abstract_inverted_index":{"We":[0,56,93],"use":[1],"Monte":[2],"Carlo":[3],"data":[4],"for":[5,32],"the":[6,11,21,44,50,84,98,108,112,120,133],"three-dimensional":[7],"Ising":[8,135],"model":[9],"at":[10],"critical":[12],"temperature":[13],"to":[14,42,80,88,107],"predict":[15],"an":[16,37,127],"emergent":[17],"radial":[18],"geometry":[19,122],"of":[20,49,78,91,123],"bulk":[22,121],"using":[23],"machine":[24],"learning.":[25],"Specifically,":[26],"we":[27],"employ":[28],"a":[29,33,59,76,124,141],"differentiable":[30],"solver":[31],"probe":[34],"field":[35],"on":[36],"asymptotically":[38],"$\\mathrm{AdS}_4$":[39],"background,":[40],"trained":[41],"reproduce":[43],"measured":[45],"momentum-space":[46],"two-point":[47],"functions":[48],"boundary":[51],"operators":[52,100],"($\u03c3$":[53],"and":[54,101,111],"$\u03b5$).":[55],"find":[57],"that":[58,103,119],"single":[60,142],"metric":[61],"cannot":[62],"simultaneously":[63],"serve":[64],"both":[65],"operators.":[66],"Fitting":[67],"each":[68],"channel":[69],"separately":[70],"improves":[71],"its":[72],"own":[73],"residual":[74],"by":[75,86,140],"factor":[77],"three":[79],"five,":[81],"but":[82],"degrades":[83],"other":[85],"up":[87],"two":[89,99],"orders":[90],"magnitude.":[92],"quantify":[94],"this":[95],"tension":[96],"between":[97],"show":[102],"it":[104],"survives":[105],"changes":[106],"momentum":[109],"window":[110],"lattice":[113],"size.":[114],"Our":[115],"results":[116],"numerically":[117],"demonstrate":[118],"theory":[125],"with":[126],"$\\mathcal{O}(1)$":[128],"central":[129],"charge,":[130],"such":[131],"as":[132],"3D":[134],"model,":[136],"is":[137],"not":[138],"captured":[139],"classical":[143],"metric.":[144]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-19T00:00:00"}
