{"id":"https://openalex.org/W2963596652","doi":"https://doi.org/10.48550/arxiv.hep-th/9607053","title":"Anticommuting Integrals and Fermionic Field Theories for Two-Dimensional Ising Models","display_name":"Anticommuting Integrals and Fermionic Field Theories for Two-Dimensional Ising Models","publication_year":1996,"publication_date":"1996-07-07","ids":{"openalex":"https://openalex.org/W2963596652","doi":"https://doi.org/10.48550/arxiv.hep-th/9607053","mag":"2963596652"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:hep-th/9607053","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/hep-th/9607053","pdf_url":"https://arxiv.org/pdf/hep-th/9607053","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/hep-th/9607053","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069840094","display_name":"V. N. Plechko","orcid":"https://orcid.org/0000-0002-8441-4598","observed_orcids":["https://orcid.org/0000-0002-8441-4598"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Plechko, V. N.","raw_affiliation_strings":["Bogoliubov Lab Dubna"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bogoliubov Lab Dubna","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5069840094"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"443","last_page":"450"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.9746000170707703,"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":0.9746000170707703,"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/T11804","display_name":"Quantum many-body systems","score":0.009800000116229057,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.0026000000070780516,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/2d-ising-model","display_name":"two-dimensional Ising model","score":0.9129999876022339},{"id":"https://openalex.org/keywords/grassmann-variables","display_name":"Grassmann variables","score":0.7900000214576721},{"id":"https://openalex.org/keywords/exact-partition-function","display_name":"exact partition function","score":0.6159999966621399},{"id":"https://openalex.org/keywords/critical-points","display_name":"critical points","score":0.8149999976158142},{"id":"https://openalex.org/keywords/continuum-limit","display_name":"continuum limit","score":0.6460000276565552},{"id":"https://openalex.org/keywords/lattice-spin-models","display_name":"lattice spin models","score":0.4860000014305115},{"id":"https://openalex.org/keywords/critical-exponents","display_name":"critical exponents","score":0.5210000276565552}],"concepts":[{"id":"https://openalex.org/C51329190","wikidata":"https://www.wikidata.org/wiki/Q1076349","display_name":"Ising model","level":2,"score":0.8585473895072937},{"id":"https://openalex.org/C49005734","wikidata":"https://www.wikidata.org/wiki/Q7581981","display_name":"Square-lattice Ising model","level":3,"score":0.7779354453086853},{"id":"https://openalex.org/C70139506","wikidata":"https://www.wikidata.org/wiki/Q1060321","display_name":"Gaussian integral","level":2,"score":0.5881614089012146},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5613524317741394},{"id":"https://openalex.org/C2778761060","wikidata":"https://www.wikidata.org/wiki/Q6714234","display_name":"MAJORANA","level":3,"score":0.49095967411994934},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.4220823645591736},{"id":"https://openalex.org/C52233224","wikidata":"https://www.wikidata.org/wiki/Q44363","display_name":"Fermion","level":2,"score":0.40949729084968567},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.325153648853302},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31148678064346313},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09646889567375183}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:arXiv.org:hep-th/9607053","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/hep-th/9607053","pdf_url":"https://arxiv.org/pdf/hep-th/9607053","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":"pmh:oai:cds.cern.ch:306696","doi":null,"is_oa":false,"landing_page_url":"http://cds.cern.ch/record/306696","pdf_url":null,"source":{"id":"https://openalex.org/S4306402195","display_name":"CERN Document Server (European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},{"id":"doi:10.48550/arxiv.hep-th/9607053","doi":"https://doi.org/10.48550/arxiv.hep-th/9607053","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.hep-th/9607053","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":"article-journal"},{"id":"mag:2963596652","doi":null,"is_oa":false,"landing_page_url":"http://inspirehep.net/record/406473","pdf_url":null,"source":{"id":"https://openalex.org/S4306523141","display_name":"Presented at","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"Presented at","raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:hep-th/9607053","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/hep-th/9607053","pdf_url":"https://arxiv.org/pdf/hep-th/9607053","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/W2963596652.pdf","grobid_xml":"https://content.openalex.org/works/W2963596652.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W1498924426","https://openalex.org/W2005585454","https://openalex.org/W2009641523","https://openalex.org/W2043570766","https://openalex.org/W2062712855","https://openalex.org/W2101531402","https://openalex.org/W2113776651","https://openalex.org/W2991334544"],"related_works":["https://openalex.org/W3042213755","https://openalex.org/W2122279635","https://openalex.org/W1989739659","https://openalex.org/W4394642728","https://openalex.org/W7095186520","https://openalex.org/W3041476160","https://openalex.org/W7100035855","https://openalex.org/W1536349052","https://openalex.org/W2572621751","https://openalex.org/W2264518009"],"abstract_inverted_index":{"We":[0],"review":[1],"the":[2,5,15,19,23,37,44,48,58,62,66,73,82,91,104,114,123,126,140,143,151,156,168,178,182,187,191,201,216,223,246,250,253],"applications":[3],"of":[4,43,47,61,79,94,128,139,155,167,181,194,213,228,252],"integral":[6,68],"over":[7],"anticommuting":[8],"Grassmann":[9],"variables":[10,96],"(nonquantum":[11],"fermionic":[12,38,95],"fields)":[13],"to":[14,113,150,177],"analytic":[16,101],"solutions":[17,102],"and":[18,86,89,122,190],"field-theoretical":[20,153,247],"formulations":[21],"for":[22,69,76,103,186,231],"2D":[24,28,49,106,157,224,232,239],"Ising":[25,29,50,107,158,233,240],"models.":[26,159,234],"The":[27,41,100,120,160,173,196,235],"model":[30],"partition":[31],"function":[32],"$Q$":[33,70],"is":[34,52,200],"presentable":[35],"as":[36,221],"Gaussian":[39,67],"integral.":[40],"use":[42],"spin-polynomial":[45,59,137],"interpretation":[46,60,134,154],"problem":[51],"stressed,":[53],"in":[54,72,215,245,249],"particular.":[55],"Starting":[56],"with":[57,90,206],"local":[63],"Boltzmann":[64],"weights,":[65],"appears":[71],"universal":[74],"form":[75],"a":[77,118],"variety":[78],"lattices,":[80,88],"including":[81],"standard":[83],"rectangular,":[84],"triangular,":[85],"hexagonal":[87],"minimal":[92],"number":[93],"(two":[97],"per":[98],"site).":[99],"correspondent":[105],"models":[108,170],"then":[109,148],"follow":[110],"by":[111],"passing":[112],"momentum":[115],"space":[116],"on":[117,125],"lattice.":[119],"symmetries":[121],"question":[124],"location":[127],"critical":[129],"point":[130],"have":[131],"an":[132],"interesting":[133],"within":[135],"this":[136],"formulation":[138],"problem.":[141],"From":[142],"exact":[144,183],"lattice":[145],"theory":[146,162,184,199,227],"we":[147,219],"pass":[149],"continuum-limit":[152],"continuum":[161,174],"captures":[163],"all":[164],"relevant":[165],"features":[166],"original":[169],"near":[171],"$T_c$.":[172,210],"limit":[175],"corresponds":[176],"low-momentum":[179],"sector":[180],"responsible":[185],"critical-point":[188],"singularities":[189],"large-distance":[192],"behaviour":[193],"correlations.":[195],"resulting":[197],"field":[198,226],"massive":[202],"two-component":[203],"Majorana":[204,217],"theory,":[205],"mass":[207],"vanishing":[208],"at":[209],"By":[211],"doubling":[212],"fermions":[214,230],"representation,":[218],"obtain":[220],"well":[222],"Dirac":[225],"charged":[229],"differences":[236],"between":[237],"particular":[238],"lattices":[241],"are":[242],"merely":[243],"adsorbed,":[244],"formulation,":[248],"definition":[251],"effective":[254],"mass.":[255]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2019-07-30T00:00:00"}