{"id":"https://openalex.org/W1622775971","doi":"https://doi.org/10.1109/isit.2015.7282859","title":"The ising model: Kramers-Wannier duality and normal factor graphs","display_name":"The ising model: Kramers-Wannier duality and normal factor graphs","publication_year":2015,"publication_date":"2015-06-01","ids":{"openalex":"https://openalex.org/W1622775971","doi":"https://doi.org/10.1109/isit.2015.7282859","mag":"1622775971"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2015.7282859","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2015.7282859","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090983465","display_name":"Ali Al-Bashabsheh","orcid":"https://orcid.org/0000-0003-0462-7727"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ali Al-Bashabsheh","raw_affiliation_strings":["Institute of Network Coding, The Chinese University of Hong Kong, Shatin N.T., Hong Kong","Institute of Network Coding, The Chinese University of Hong Kong, Shatin, N. T., Hong Kong"],"affiliations":[{"raw_affiliation_string":"Institute of Network Coding, The Chinese University of Hong Kong, Shatin N.T., Hong Kong","institution_ids":["https://openalex.org/I177725633"]},{"raw_affiliation_string":"Institute of Network Coding, The Chinese University of Hong Kong, Shatin, N. T., Hong Kong","institution_ids":["https://openalex.org/I177725633"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028154201","display_name":"Pascal O. Vontobel","orcid":"https://orcid.org/0000-0002-6180-258X"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Pascal O. Vontobel","raw_affiliation_strings":["Dept. of Information Engineering, The Chinese University of Hong Kong, Shatin N.T., Hong Kong","Department of Information Engineering, The Chinese University of Hong Kong, Shatin, N. T., Hong Kong#TAB#"],"affiliations":[{"raw_affiliation_string":"Dept. of Information Engineering, The Chinese University of Hong Kong, Shatin N.T., Hong Kong","institution_ids":["https://openalex.org/I177725633"]},{"raw_affiliation_string":"Department of Information Engineering, The Chinese University of Hong Kong, Shatin, N. T., Hong Kong#TAB#","institution_ids":["https://openalex.org/I177725633"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5090983465"],"corresponding_institution_ids":["https://openalex.org/I177725633"],"apc_list":null,"apc_paid":null,"fwci":1.7218,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.84579656,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"2","issue":null,"first_page":"2266","last_page":"2270"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.996999979019165,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.996999979019165,"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/T10591","display_name":"Theoretical and Computational Physics","score":0.993399977684021,"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":0.9916999936103821,"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":[{"id":"https://openalex.org/keywords/ising-model","display_name":"Ising model","score":0.7756460905075073},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.6785953044891357},{"id":"https://openalex.org/keywords/square-lattice-ising-model","display_name":"Square-lattice Ising model","score":0.5719356536865234},{"id":"https://openalex.org/keywords/wannier-function","display_name":"Wannier function","score":0.5620783567428589},{"id":"https://openalex.org/keywords/factor-graph","display_name":"Factor graph","score":0.5557504892349243},{"id":"https://openalex.org/keywords/partition-function","display_name":"Partition function (quantum field theory)","score":0.5313706398010254},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46315330266952515},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.4549223780632019},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.44664981961250305},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.42217913269996643},{"id":"https://openalex.org/keywords/factor","display_name":"Factor (programming language)","score":0.42165184020996094},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3495030403137207},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2985706627368927},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.2935435175895691},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2587543725967407},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.23113054037094116},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.10022860765457153}],"concepts":[{"id":"https://openalex.org/C51329190","wikidata":"https://www.wikidata.org/wiki/Q1076349","display_name":"Ising model","level":2,"score":0.7756460905075073},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.6785953044891357},{"id":"https://openalex.org/C49005734","wikidata":"https://www.wikidata.org/wiki/Q7581981","display_name":"Square-lattice Ising model","level":3,"score":0.5719356536865234},{"id":"https://openalex.org/C14022793","wikidata":"https://www.wikidata.org/wiki/Q1152058","display_name":"Wannier function","level":2,"score":0.5620783567428589},{"id":"https://openalex.org/C159246509","wikidata":"https://www.wikidata.org/wiki/Q5428725","display_name":"Factor graph","level":3,"score":0.5557504892349243},{"id":"https://openalex.org/C2778401447","wikidata":"https://www.wikidata.org/wiki/Q7140637","display_name":"Partition function (quantum field theory)","level":2,"score":0.5313706398010254},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46315330266952515},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.4549223780632019},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.44664981961250305},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.42217913269996643},{"id":"https://openalex.org/C2781039887","wikidata":"https://www.wikidata.org/wiki/Q1391724","display_name":"Factor (programming language)","level":2,"score":0.42165184020996094},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3495030403137207},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2985706627368927},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.2935435175895691},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2587543725967407},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.23113054037094116},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.10022860765457153},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit.2015.7282859","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2015.7282859","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.4300000071525574}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1488574293","https://openalex.org/W1489896549","https://openalex.org/W1530042113","https://openalex.org/W1647408933","https://openalex.org/W1970635910","https://openalex.org/W2000512161","https://openalex.org/W2055496088","https://openalex.org/W2138628599","https://openalex.org/W2139584447","https://openalex.org/W2171516545","https://openalex.org/W2225144138","https://openalex.org/W2486762503","https://openalex.org/W2963518415","https://openalex.org/W3098086435","https://openalex.org/W6629196920"],"related_works":["https://openalex.org/W3209539671","https://openalex.org/W4288357902","https://openalex.org/W2944617580","https://openalex.org/W2382664089","https://openalex.org/W2000567571","https://openalex.org/W2028559712","https://openalex.org/W2028703046","https://openalex.org/W2787138325","https://openalex.org/W1985264093","https://openalex.org/W2047006621"],"abstract_inverted_index":{"In":[0],"the":[1,4,9,13,17,24,33],"light":[2],"of":[3,12,28],"recent":[5],"interest":[6],"in":[7,45],"approximating":[8],"partition":[10],"function":[11],"Ising":[14],"model":[15],"using":[16],"dual":[18,34],"normal":[19,35],"factor":[20,36],"graph,":[21],"we":[22],"revisit":[23],"classical":[25],"duality":[26],"result":[27],"Kramers":[29],"and":[30],"Wannier,":[31],"where":[32],"graph":[37],"may":[38],"be":[39],"viewed":[40],"as":[41],"an":[42],"intermediate":[43],"step":[44],"establishing":[46],"such":[47],"a":[48],"result.":[49]},"counts_by_year":[{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}