{"id":"https://openalex.org/W7225266286","doi":"https://doi.org/10.48550/arxiv.2611.04165","title":"The Arc Threshold of the Two-Row Ising Torus: Exact Factorization, an Algebraic Critical Coupling, Uniformity in the Circumference, and the Rate of Convergence","display_name":"The Arc Threshold of the Two-Row Ising Torus: Exact Factorization, an Algebraic Critical Coupling, Uniformity in the Circumference, and the Rate of Convergence","publication_year":2026,"publication_date":"2026-11-03","ids":{"openalex":"https://openalex.org/W7225266286","doi":"https://doi.org/10.48550/arxiv.2611.04165"},"language":"en","primary_location":{"id":"doi:10.48550/arxiv.2611.04165","doi":"https://doi.org/10.48550/arxiv.2611.04165","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2611.04165","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"},"volume":null,"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2611.04165","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5127881284","display_name":"Marco Mandap","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I242692392","display_name":"Bulacan State University","ror":"https://ror.org/01c5aqg65","country_code":"PH","type":"education","lineage":["https://openalex.org/I242692392"]}],"countries":["PH"],"is_corresponding":true,"raw_author_name":"Mandap, Marco","raw_affiliation_strings":["Bulacan State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bulacan State University","institution_ids":["https://openalex.org/I242692392"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5127881284"],"corresponding_institution_ids":["https://openalex.org/I242692392"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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":0.7935000061988831,"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":0.7935000061988831,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.08709999918937683,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T13234","display_name":"p-Adic Analysis and Mathematical Physics","score":0.05550000071525574,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7771999835968018},{"id":"https://openalex.org/C126875415","wikidata":"https://www.wikidata.org/wiki/Q203425","display_name":"Unit circle","level":2,"score":0.7350000143051147},{"id":"https://openalex.org/C51329190","wikidata":"https://www.wikidata.org/wiki/Q1076349","display_name":"Ising model","level":2,"score":0.6614000201225281},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.5861999988555908},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.5085999965667725},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.5040000081062317},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.47769999504089355},{"id":"https://openalex.org/C2778401447","wikidata":"https://www.wikidata.org/wiki/Q7140637","display_name":"Partition function (quantum field theory)","level":2,"score":0.4771000146865845},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.43389999866485596},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.40380001068115234},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.3928000032901764},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.38670000433921814},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.38449999690055847},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.38089999556541443},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3578000068664551},{"id":"https://openalex.org/C83415579","wikidata":"https://www.wikidata.org/wiki/Q161973","display_name":"Arc (geometry)","level":2,"score":0.3499000072479248},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.3495999872684479},{"id":"https://openalex.org/C49005734","wikidata":"https://www.wikidata.org/wiki/Q7581981","display_name":"Square-lattice Ising model","level":3,"score":0.33970001339912415},{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.3379000127315521},{"id":"https://openalex.org/C9555016","wikidata":"https://www.wikidata.org/wiki/Q828111","display_name":"Zero divisor","level":2,"score":0.33559998869895935},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.3330000042915344},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32420000433921814},{"id":"https://openalex.org/C207043602","wikidata":"https://www.wikidata.org/wiki/Q266237","display_name":"Algebraic curve","level":2,"score":0.31790000200271606},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.30889999866485596},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.3061999976634979},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29820001125335693},{"id":"https://openalex.org/C183276030","wikidata":"https://www.wikidata.org/wiki/Q1193095","display_name":"Coupling constant","level":2,"score":0.29750001430511475},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.290800005197525},{"id":"https://openalex.org/C35235930","wikidata":"https://www.wikidata.org/wiki/Q187235","display_name":"Riemann zeta function","level":2,"score":0.2775000035762787},{"id":"https://openalex.org/C89290136","wikidata":"https://www.wikidata.org/wiki/Q550791","display_name":"Algebraic extension","level":5,"score":0.27149999141693115},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.2612000107765198},{"id":"https://openalex.org/C84316537","wikidata":"https://www.wikidata.org/wiki/Q36255","display_name":"Unit vector","level":2,"score":0.2549000084400177},{"id":"https://openalex.org/C65682993","wikidata":"https://www.wikidata.org/wiki/Q1056451","display_name":"Reflection (computer programming)","level":2,"score":0.25459998846054077},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.2515000104904175},{"id":"https://openalex.org/C47177299","wikidata":"https://www.wikidata.org/wiki/Q2390323","display_name":"Unit disk","level":2,"score":0.2506999969482422}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2611.04165","doi":"https://doi.org/10.48550/arxiv.2611.04165","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2611.04165","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":"doi:10.48550/arxiv.2611.04165","doi":"https://doi.org/10.48550/arxiv.2611.04165","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2611.04165","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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0,17,136],"Lee-Yang":[1],"circle":[2,31],"theorem":[3,32],"places":[4],"every":[5,21,102],"zero":[6,22],"of":[7,41,65,95],"a":[8,34,78,103],"ferromagnetic":[9],"Ising":[10,57],"partition":[11],"polynomial":[12],"on":[13],"the":[14,25,30,38,42,54,61,66,71,83,90,107,121,127,139,149],"unit":[15],"circle.":[16],"arc":[18,108],"condition,":[19],"that":[20,101,114,120],"lie":[23],"in":[24,93,144],"closed":[26],"left":[27],"half-plane,":[28],"turns":[29],"into":[33],"product":[35],"formula":[36],"for":[37,49,111],"characteristic":[39],"function":[40],"occupation":[43],"count":[44],"and":[45,81,119,138,155],"makes":[46],"it":[47],"usable":[48],"local":[50],"limit":[51],"theorems.":[52],"For":[53],"two-row":[55],"periodic":[56],"torus":[58],"we":[59],"give":[60],"exact":[62],"reflection":[63],"factorization":[64,137],"row":[67],"transfer":[68],"matrix,":[69],"reduce":[70],"crossing":[72],"at":[73,126],"zeta":[74,150],"=":[75,87,151],"i":[76,152],"to":[77],"real":[79],"cubic,":[80],"identify":[82],"critical":[84],"coupling":[85,117],"a_c*":[86,105,125],"0.8637850566870...":[88],"as":[89],"unique":[91],"root":[92],"(0,1)":[94],"an":[96,131],"explicit":[97,132],"octic.":[98],"We":[99],"prove":[100],">":[104],"satisfies":[106],"condition":[109],"simultaneously":[110],"all":[112],"circumferences,":[113],"no":[115],"smaller":[116],"does,":[118],"finite":[122],"thresholds":[123],"approach":[124],"rate":[128,156],"C/n^2":[129],"with":[130],"algebraic":[133],"constant":[134],"C.":[135],"2x2":[140],"threshold":[141],"are":[142,157],"formalized":[143],"Lean":[145],"4":[146],"against":[147],"Mathlib;":[148],"reduction,":[153],"uniformity":[154],"analysis-level.":[158]},"counts_by_year":[],"updated_date":"2026-11-05T12:25:35.769452","created_date":"2026-11-05T00:00:00"}