{"id":"https://openalex.org/W4403662012","doi":"https://doi.org/10.48550/arxiv.2409.08693","title":"Boolean SK Model","display_name":"Boolean SK Model","publication_year":2024,"publication_date":"2024-09-13","ids":{"openalex":"https://openalex.org/W4403662012","doi":"https://doi.org/10.48550/arxiv.2409.08693"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2409.08693","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2409.08693","pdf_url":"https://arxiv.org/pdf/2409.08693","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2409.08693","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005761274","display_name":"Linda Albanese","orcid":"https://orcid.org/0000-0003-1783-0775","observed_orcids":["https://orcid.org/0000-0003-1783-0775"]},"institutions":[{"id":"https://openalex.org/I142910587","display_name":"University of Salento","ror":"https://ror.org/03fc1k060","country_code":"IT","type":"education","lineage":["https://openalex.org/I142910587"]},{"id":"https://openalex.org/I4210095193","display_name":"Istituto Nazionale di Fisica Nucleare, Sezione di Lecce","ror":"https://ror.org/00qrf6g60","country_code":"IT","type":"facility","lineage":["https://openalex.org/I160013858","https://openalex.org/I4210095193"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Albanese, Linda","raw_affiliation_strings":["Department of Mathematics and Physics , University of Salento , Italy","Istituto Nazionale di Fisica Nucleare , Sezione di Lecce , Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Physics , University of Salento , Italy","institution_ids":["https://openalex.org/I142910587"]},{"raw_affiliation_string":"Istituto Nazionale di Fisica Nucleare , Sezione di Lecce , Italy","institution_ids":["https://openalex.org/I4210095193"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077516005","display_name":"Andrea Alessandrelli","orcid":"https://orcid.org/0000-0003-4583-1417","observed_orcids":["https://orcid.org/0000-0003-4583-1417"]},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]},{"id":"https://openalex.org/I4210095193","display_name":"Istituto Nazionale di Fisica Nucleare, Sezione di Lecce","ror":"https://ror.org/00qrf6g60","country_code":"IT","type":"facility","lineage":["https://openalex.org/I160013858","https://openalex.org/I4210095193"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Alessandrelli, Andrea","raw_affiliation_strings":["Department of Computer Science , University of Pisa , Italy","Istituto Nazionale di Fisica Nucleare , Sezione di Lecce , Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science , University of Pisa , Italy","institution_ids":["https://openalex.org/I108290504"]},{"raw_affiliation_string":"Istituto Nazionale di Fisica Nucleare , Sezione di Lecce , Italy","institution_ids":["https://openalex.org/I4210095193"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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":0.9351000189781189,"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":0.9351000189781189,"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/T10474","display_name":"Material Dynamics and Properties","score":0.022099999710917473,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.010200000368058681,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/sherrington-kirkpatrick-model","display_name":"Sherrington-Kirkpatrick model","score":0.9760000109672546},{"id":"https://openalex.org/keywords/mean-field-theory","display_name":"mean-field theory","score":0.5830000042915344},{"id":"https://openalex.org/keywords/replica-symmetry-breaking","display_name":"replica symmetry breaking","score":0.8009999990463257},{"id":"https://openalex.org/keywords/de-almeida-thouless-line","display_name":"de Almeida-Thouless line","score":0.9900000095367432},{"id":"https://openalex.org/keywords/thermodynamic-limit","display_name":"thermodynamic limit","score":0.8830000162124634},{"id":"https://openalex.org/keywords/glassy-phase","display_name":"glassy phase","score":0.6729999780654907},{"id":"https://openalex.org/keywords/ising-spin-glass","display_name":"Ising spin glass","score":0.531000018119812},{"id":"https://openalex.org/keywords/random-neural-networks","display_name":"random neural networks","score":0.35100001096725464}],"concepts":[{"id":"https://openalex.org/C150775274","wikidata":"https://www.wikidata.org/wiki/Q1490646","display_name":"Spin glass","level":2,"score":0.7911184430122375},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5773782730102539},{"id":"https://openalex.org/C42704618","wikidata":"https://www.wikidata.org/wiki/Q910917","display_name":"Spin (aerodynamics)","level":2,"score":0.4948498606681824},{"id":"https://openalex.org/C202213908","wikidata":"https://www.wikidata.org/wiki/Q626011","display_name":"Mean field theory","level":2,"score":0.4422643184661865},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.39672738313674927},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.39620140194892883},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3601072430610657},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3548545837402344},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.13479000329971313},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.12057492136955261}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2409.08693","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2409.08693","pdf_url":"https://arxiv.org/pdf/2409.08693","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2409.08693","doi":"https://doi.org/10.48550/arxiv.2409.08693","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2409.08693","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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2409.08693","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2409.08693","pdf_url":"https://arxiv.org/pdf/2409.08693","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320334080","display_name":"Gruppo Nazionale per la Fisica Matematica","ror":"https://ror.org/01d6bq278"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4403662012.pdf","grobid_xml":"https://content.openalex.org/works/W4403662012.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2160109699","https://openalex.org/W1591585849","https://openalex.org/W1979521946","https://openalex.org/W2089251571","https://openalex.org/W2005755451","https://openalex.org/W2007803385","https://openalex.org/W2071510302","https://openalex.org/W4294216976","https://openalex.org/W2324200842","https://openalex.org/W2030455904"],"abstract_inverted_index":{"For":[0],"over":[1],"half":[2],"a":[3,12,40,87,115,201,206],"century,":[4],"statistical":[5],"mechanics":[6],"of":[7,32,43,48,71,90,145],"spin":[8],"glasses":[9],"played":[10],"as":[11,54,58,99,185],"paradigm":[13],"to":[14,24,65,75,94,98,105,205],"model":[15,103,120,197],"and":[16,131,157,169,195],"interpret":[17],"disparate":[18],"phenomena,":[19],"ranging":[20],"from":[21,200],"quantitative":[22],"biology":[23],"computer":[25],"science.":[26],"However,":[27],"despite":[28],"the":[29,46,55,82,91,100,110,125,128,132,143,146,152,175,181,186,196],"extensive":[30],"body":[31],"research":[33],"in":[34,60,174],"this":[35,63,72,77,119],"area,":[36],"there":[37],"is":[38,67,74,188],"still":[39],"notable":[41],"lack":[42],"studies":[44],"addressing":[45],"replacement":[47],"Ising":[49,182],"spins":[50],"with":[51,109,180],"Boolean":[52,101],"spins:":[53],"latter":[56],"play":[57],"bits":[59],"Machine":[61],"Learning,":[62],"gap":[64],"fill":[66],"now":[68],"mandatory.":[69],"Purpose":[70],"paper":[73],"address":[76],"study":[78],"by":[79,121,166],"focusing":[80],"on":[81],"mean":[83],"field":[84],"assumption,":[85],"providing":[86],"comprehensive":[88,116],"description":[89],"results":[92],"pertaining":[93],"these":[95],"networks,":[96],"referred":[97],"SK":[102,111,183],"due":[104],"their":[106],"close":[107],"relationship":[108],"one.":[112],"We":[113],"provide":[114],"framework":[117],"for":[118],"employing":[122],"Guerra":[123],"interpolation:":[124],"thermodynamic":[126],"limit,":[127],"replica":[129,134,147],"symmetric":[130],"broken":[133],"free":[135],"energy":[136],"expressions":[137],"are":[138,164,193],"derived.":[139],"Further,":[140],"we":[141],"inspect":[142],"onset":[144],"symmetry":[148],"breaking":[149],"--":[150,156],"i.e.,":[151],"de":[153],"Almeida-Thouless":[154],"line":[155],"derive":[158],"Ghirlanda-Guerra":[159],"fluctuations.":[160],"All":[161],"theoretical":[162],"findings":[163],"corroborated":[165],"numerical":[167],"inspections":[168],"both":[170],"highlight":[171],"crucial":[172],"differences":[173],"network's":[176],"behavior":[177,204],"if":[178],"compared":[179],"model:":[184],"temperature":[187],"lowered,":[189],"no":[190],"phase":[191],"transitions":[192],"evidenced":[194],"continuously":[198],"moves":[199],"random":[202],"(ergodic)":[203],"disordered":[207],"(glassy)":[208],"phase.":[209]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-09-30T09:27:27.532063","created_date":"2024-10-23T00:00:00"}