{"id":"https://openalex.org/W2096285737","doi":"https://doi.org/10.1109/sfcs.2003.1238235","title":"The Ising model on trees: boundary conditions and mixing time","display_name":"The Ising model on trees: boundary conditions and mixing time","publication_year":2004,"publication_date":"2004-03-02","ids":{"openalex":"https://openalex.org/W2096285737","doi":"https://doi.org/10.1109/sfcs.2003.1238235","mag":"2096285737"},"language":"en","primary_location":{"id":"doi:10.1109/sfcs.2003.1238235","is_oa":false,"landing_page_url":"https://doi.org/10.1109/sfcs.2003.1238235","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings.","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/A5021815654","display_name":"Fabio Martinelli","orcid":"https://orcid.org/0000-0001-6746-4967"},"institutions":[{"id":"https://openalex.org/I119003972","display_name":"Roma Tre University","ror":"https://ror.org/05vf0dg29","country_code":"IT","type":"education","lineage":["https://openalex.org/I119003972"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"F. Martinelli","raw_affiliation_strings":["Department of Mathematics, University of Rome Tre, Rome, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Rome Tre, Rome, Italy","institution_ids":["https://openalex.org/I119003972"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020315523","display_name":"Alistair Sinclair","orcid":"https://orcid.org/0009-0002-9210-268X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. Sinclair","raw_affiliation_strings":["Computer Science Division, University of California, CA, USA"],"affiliations":[{"raw_affiliation_string":"Computer Science Division, University of California, CA, USA","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076599508","display_name":"Dror Weitz","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"D. Weitz","raw_affiliation_strings":["Computer Science Division, University of California, CA, USA"],"affiliations":[{"raw_affiliation_string":"Computer Science Division, University of California, CA, USA","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5021815654"],"corresponding_institution_ids":["https://openalex.org/I119003972"],"apc_list":null,"apc_paid":null,"fwci":4.4865,"has_fulltext":false,"cited_by_count":40,"citation_normalized_percentile":{"value":0.95182532,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"628","last_page":"639"},"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":0.9995999932289124,"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":0.9995999932289124,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9983999729156494,"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/T10591","display_name":"Theoretical and Computational Physics","score":0.9940000176429749,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/ising-model","display_name":"Ising model","score":0.7379878759384155},{"id":"https://openalex.org/keywords/mixing","display_name":"Mixing (physics)","score":0.7267683148384094},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5470163226127625},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4930736720561981},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4536426067352295},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.305987685918808},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2789013683795929},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14069387316703796},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0648500919342041}],"concepts":[{"id":"https://openalex.org/C51329190","wikidata":"https://www.wikidata.org/wiki/Q1076349","display_name":"Ising model","level":2,"score":0.7379878759384155},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.7267683148384094},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5470163226127625},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4930736720561981},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4536426067352295},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.305987685918808},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2789013683795929},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14069387316703796},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0648500919342041}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/sfcs.2003.1238235","is_oa":false,"landing_page_url":"https://doi.org/10.1109/sfcs.2003.1238235","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings.","raw_type":"proceedings-article"},{"id":"pmh:oai:berkeley.edu:13030-hb5290088p","is_oa":false,"landing_page_url":"http://techreports.lib.berkeley.edu/accessPages/CSD-03-1256.html","pdf_url":null,"source":{"id":"https://openalex.org/S7407050879","display_name":"UC Berkeley","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"technical reports"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.122.3049","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.122.3049","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mat.uniroma3.it/users/martin/PAPERS/Focs.ps","raw_type":"text"},{"id":"pmh:oai:iris.uniroma3.it:11590/184564","is_oa":false,"landing_page_url":"http://hdl.handle.net/11590/184564","pdf_url":null,"source":{"id":"https://openalex.org/S4377196120","display_name":"Iris (Roma Tre University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119003972","host_organization_name":"Roma Tre University","host_organization_lineage":["https://openalex.org/I119003972"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W26421094","https://openalex.org/W34780633","https://openalex.org/W182345440","https://openalex.org/W1494720687","https://openalex.org/W1496074149","https://openalex.org/W1507653385","https://openalex.org/W1530042113","https://openalex.org/W1539201265","https://openalex.org/W1556987501","https://openalex.org/W1582818251","https://openalex.org/W1582932802","https://openalex.org/W1976445742","https://openalex.org/W1977007046","https://openalex.org/W1981764507","https://openalex.org/W1988381794","https://openalex.org/W1988928480","https://openalex.org/W1991354024","https://openalex.org/W1996199671","https://openalex.org/W1997280309","https://openalex.org/W2011373957","https://openalex.org/W2017816219","https://openalex.org/W2022380818","https://openalex.org/W2024718189","https://openalex.org/W2026311717","https://openalex.org/W2030932831","https://openalex.org/W2037616236","https://openalex.org/W2043509032","https://openalex.org/W2049825392","https://openalex.org/W2062822698","https://openalex.org/W2064378620","https://openalex.org/W2073608764","https://openalex.org/W2086852576","https://openalex.org/W2088794759","https://openalex.org/W2092260192","https://openalex.org/W2096285737","https://openalex.org/W2103470671","https://openalex.org/W2106668810","https://openalex.org/W2135481845","https://openalex.org/W2155597422","https://openalex.org/W2163208395","https://openalex.org/W2168256531","https://openalex.org/W2237678354","https://openalex.org/W2279676320","https://openalex.org/W2582449852","https://openalex.org/W2611336766","https://openalex.org/W2963923339","https://openalex.org/W3099943025","https://openalex.org/W3105827348","https://openalex.org/W4205240937","https://openalex.org/W4285719527","https://openalex.org/W6659984009"],"related_works":["https://openalex.org/W2935759653","https://openalex.org/W3105167352","https://openalex.org/W54078636","https://openalex.org/W2954470139","https://openalex.org/W1501425562","https://openalex.org/W2902782467","https://openalex.org/W4255387243","https://openalex.org/W2090368795","https://openalex.org/W758601826","https://openalex.org/W1979989913"],"abstract_inverted_index":{"We":[0,67],"give":[1],"the":[2,7,13,17,21,28,49,54,77,94,98,102,115,119,126,146,155],"first":[3],"comprehensive":[4],"analysis":[5],"of":[6,9,16,79,101,138],"effect":[8],"boundary":[10,38,51,127],"conditions":[11],"on":[12,31,93],"mixing":[14,29,55,116],"time":[15,30,56,117],"Glauber":[18],"dynamics":[19],"for":[20,114],"Ising":[22],"model.":[23],"Specifically,":[24],"we":[25],"show":[26,69],"that":[27,70],"an":[32,80],"n-vertex":[33],"regular":[34],"tree":[35],"with":[36,142],"(+)":[37],"remains":[39],"O(n":[40],"log":[41],"n)":[42],"at":[43,64,150],"all":[44],"temperatures":[45],"(in":[46],"contrast":[47],"to":[48,74,125,133],"free":[50],"case,":[52],"where":[53,121],"is":[57,123],"not":[58],"bounded":[59],"by":[60],"any":[61],"fixed":[62],"polynomial":[63],"low":[65],"temperatures).":[66],"also":[68,131],"this":[71],"bound":[72],"continues":[73],"hold":[75],"in":[76,118],"presence":[78],"arbitrary":[81],"external":[82],"field.":[83],"Our":[84,129],"results":[85,113],"are":[86],"actually":[87],"stronger,":[88],"and":[89,97,111,154],"provide":[90],"tight":[91],"bounds":[92],"log-Sobolev":[95],"constant":[96],"spectral":[99],"gap":[100],"dynamics.":[103],"In":[104],"addition,":[105],"our":[106],"methods":[107],"yield":[108],"simpler":[109],"proofs":[110],"stronger":[112],"regime":[120],"it":[122],"insensitive":[124],"condition.":[128],"techniques":[130],"apply":[132],"a":[134],"much":[135],"wider":[136],"class":[137],"models,":[139],"including":[140],"those":[141],"hard":[143],"constraints":[144],"like":[145],"antiferromagnetic":[147],"Potts":[148],"model":[149,157],"zero":[151],"temperature":[152],"(colorings)":[153],"hard-core":[156],"(independent":[158],"sets).":[159]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
