{"id":"https://openalex.org/W2052494313","doi":"https://doi.org/10.1103/physreva.43.1079","title":"Phase transitions in a dynamic model of neural networks","display_name":"Phase transitions in a dynamic model of neural networks","publication_year":1991,"publication_date":"1991-01-01","ids":{"openalex":"https://openalex.org/W2052494313","doi":"https://doi.org/10.1103/physreva.43.1079","mag":"2052494313","pmid":"https://pubmed.ncbi.nlm.nih.gov/9905124"},"language":"en","primary_location":{"id":"doi:10.1103/physreva.43.1079","doi":"https://doi.org/10.1103/physreva.43.1079","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physreva.43.1079","pdf_url":null,"source":{"id":"https://openalex.org/S164566984","display_name":"Physical Review A","issn_l":"0556-2791","issn":["0556-2791","1050-2947","1094-1622","1538-4446","2469-9926","2469-9934","2469-9942"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-2","ki-jl-1","norway-2","poland-100","poland-70","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review A","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","pubmed"],"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/A5056345444","display_name":"G. M. Shim","orcid":"https://orcid.org/0000-0003-4077-3019","observed_orcids":["https://orcid.org/0000-0003-4077-3019"]},"institutions":[{"id":"https://openalex.org/I139264467","display_name":"Seoul National University","ror":"https://ror.org/04h9pn542","country_code":"KR","type":"education","lineage":["https://openalex.org/I139264467"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"G. M. Shim","raw_affiliation_strings":["Department of Physics, Seoul National University, Seoul 151-742, Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Seoul National University, Seoul 151-742, Korea","institution_ids":["https://openalex.org/I139264467"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056662128","display_name":"M. Y. Choi","orcid":"https://orcid.org/0000-0001-8070-7716","observed_orcids":["https://orcid.org/0000-0001-8070-7716"]},"institutions":[{"id":"https://openalex.org/I139264467","display_name":"Seoul National University","ror":"https://ror.org/04h9pn542","country_code":"KR","type":"education","lineage":["https://openalex.org/I139264467"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"M. Y. Choi","raw_affiliation_strings":["Department of Physics, Seoul National University, Seoul 151-742, Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Seoul National University, Seoul 151-742, Korea","institution_ids":["https://openalex.org/I139264467"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008542425","display_name":"Man-Sun Kim","orcid":"https://orcid.org/0000-0002-7791-0956","observed_orcids":["https://orcid.org/0000-0002-7791-0956"]},"institutions":[{"id":"https://openalex.org/I139264467","display_name":"Seoul National University","ror":"https://ror.org/04h9pn542","country_code":"KR","type":"education","lineage":["https://openalex.org/I139264467"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"D. Kim","raw_affiliation_strings":["Department of Physics, Seoul National University, Seoul 151-742, Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Seoul National University, Seoul 151-742, Korea","institution_ids":["https://openalex.org/I139264467"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I139264467"],"apc_list":{"value":2675,"currency":"USD","value_usd":2675},"apc_paid":null,"fwci":1.1479,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.77305353,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"43","issue":"2","first_page":"1079","last_page":"1089"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.5981000065803528,"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":0.5981000065803528,"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/T10320","display_name":"Neural Networks and Applications","score":0.19179999828338623,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.16359999775886536,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/neural-network","display_name":"artificial neural networks","score":0.824999988079071},{"id":"https://openalex.org/keywords/phase-transitions","display_name":"phase transitions","score":0.9390000104904175},{"id":"https://openalex.org/keywords/hopfield-neural-network","display_name":"Hopfield neural network","score":0.8159999847412109},{"id":"https://openalex.org/keywords/path-integral","display_name":"path integral","score":0.6489999890327454},{"id":"https://openalex.org/keywords/timescales","display_name":"time scales","score":0.6470000147819519},{"id":"https://openalex.org/keywords/refractory-period","display_name":"refractory period","score":0.8180000185966492},{"id":"https://openalex.org/keywords/action-potential-duration","display_name":"action potential duration","score":0.6800000071525574},{"id":"https://openalex.org/keywords/network-capacity","display_name":"network capacity","score":0.7940000295639038},{"id":"https://openalex.org/keywords/phase-diagram","display_name":"phase diagram","score":0.8899999856948853},{"id":"https://openalex.org/keywords/first-order-phase-transition","display_name":"first-order phase transition","score":0.9369999766349792},{"id":"https://openalex.org/keywords/second-order-phase-transition","display_name":"second-order phase transition","score":0.8029999732971191},{"id":"https://openalex.org/keywords/temperature-dependence","display_name":"temperature dependence","score":0.6800000071525574}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.8832365274429321},{"id":"https://openalex.org/C85906118","wikidata":"https://www.wikidata.org/wiki/Q186693","display_name":"Phase diagram","level":3,"score":0.7210564613342285},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6377502679824829},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.6250946521759033},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5112559795379639},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.49683669209480286},{"id":"https://openalex.org/C149288129","wikidata":"https://www.wikidata.org/wiki/Q185357","display_name":"Phase transition","level":2,"score":0.4943070411682129},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.48772868514060974},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.47906431555747986},{"id":"https://openalex.org/C186399060","wikidata":"https://www.wikidata.org/wiki/Q959962","display_name":"Diagram","level":2,"score":0.4649236500263214},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.4507175385951996},{"id":"https://openalex.org/C154018700","wikidata":"https://www.wikidata.org/wiki/Q898323","display_name":"Path integral formulation","level":3,"score":0.4209236204624176},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4103620946407318},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3253706693649292},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.24300521612167358},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22586655616760254},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2063923180103302},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1528199017047882},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.090302973985672},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08619686961174011},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.06483635306358337},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1103/physreva.43.1079","doi":"https://doi.org/10.1103/physreva.43.1079","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physreva.43.1079","pdf_url":null,"source":{"id":"https://openalex.org/S164566984","display_name":"Physical Review A","issn_l":"0556-2791","issn":["0556-2791","1050-2947","1094-1622","1538-4446","2469-9926","2469-9934","2469-9942"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-2","ki-jl-1","norway-2","poland-100","poland-70","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review A","raw_type":"journal-article"},{"id":"pmid:9905124","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/9905124","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical review. A, Atomic, molecular, and optical physics","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321038","display_name":"Fonds National de la Recherche Luxembourg","ror":"https://ror.org/039z13y21"},{"id":"https://openalex.org/F4320321292","display_name":"Seoul National University","ror":"https://ror.org/04h9pn542"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W1979243958","https://openalex.org/W1982203879","https://openalex.org/W1986786076","https://openalex.org/W1994633420","https://openalex.org/W1999192440","https://openalex.org/W2001570872","https://openalex.org/W2001951139","https://openalex.org/W2002193713","https://openalex.org/W2004925566","https://openalex.org/W2007431958","https://openalex.org/W2015272679","https://openalex.org/W2015538069","https://openalex.org/W2017739483","https://openalex.org/W2021056267","https://openalex.org/W2027424252","https://openalex.org/W2030450972","https://openalex.org/W2043014754","https://openalex.org/W2051995576","https://openalex.org/W2069129925","https://openalex.org/W2072799359","https://openalex.org/W2080277460","https://openalex.org/W2082715271","https://openalex.org/W2083517661","https://openalex.org/W2087636648","https://openalex.org/W2088899269","https://openalex.org/W2092632480","https://openalex.org/W2094498958","https://openalex.org/W2115818372","https://openalex.org/W2128084896","https://openalex.org/W4241400578","https://openalex.org/W4247650721"],"related_works":["https://openalex.org/W2015538069","https://openalex.org/W7099553147","https://openalex.org/W2072799359","https://openalex.org/W7095381463","https://openalex.org/W1992621146","https://openalex.org/W2022008179","https://openalex.org/W2074777079","https://openalex.org/W1978114227","https://openalex.org/W6995706101","https://openalex.org/W1986985455"],"abstract_inverted_index":{"A":[0],"dynamic":[1],"model":[2,44],"for":[3],"neural":[4],"networks":[5],"that":[6,40],"explicitly":[7],"takes":[8],"into":[9],"account":[10],"the":[11,19,25,34,42,50,53,57,62,70,73],"existence":[12],"of":[13,27,33,41,52,68],"several":[14],"time":[15,20],"scales":[16],"without":[17],"discretizing":[18],"is":[21,36,79],"studied":[22],"analytically":[23],"via":[24],"use":[26],"path":[28],"integrals.":[29],"The":[30,75],"maximum":[31],"capacity":[32],"network":[35],"found":[37],"to":[38,56],"be":[39],"Hopfield":[43],"divided":[45],"by":[46],"1+${\\mathit{a}}^{2}$,":[47],"with":[48],"a":[49,66],"ratio":[51],"refractory":[54],"period":[55],"action-potential":[58],"duration.":[59],"We":[60],"obtain":[61],"phase":[63,77],"diagram":[64,78],"as":[65,86,88],"function":[67],"a,":[69],"capacity,":[71],"and":[72],"temperature.":[74],"overall":[76],"rich":[80],"in":[81],"structure,":[82],"exhibiting":[83],"first-order":[84],"transitions":[85],"well":[87],"continuous":[89],"ones.":[90]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2016-06-24T00:00:00"}
