{"id":"https://openalex.org/W7204204510","doi":"https://doi.org/10.48550/arxiv.2608.22159","title":"Optimal Mixing of Glauber Dynamics for the Sherrington-Kirkpatrick Model at $\u03b2< 1/2$","display_name":"Optimal Mixing of Glauber Dynamics for the Sherrington-Kirkpatrick Model at $\u03b2< 1/2$","publication_year":2026,"publication_date":"2026-08-23","ids":{"openalex":"https://openalex.org/W7204204510","doi":"https://doi.org/10.48550/arxiv.2608.22159"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.22159","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.22159","pdf_url":"https://arxiv.org/pdf/2608.22159","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","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.22159","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5148137144","display_name":"Sihan Wang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wang, Sihan","raw_affiliation_strings":["Zhiyuan College , Shanghai Jiao Tong University , Shanghai , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Zhiyuan College , Shanghai Jiao Tong University , Shanghai , China","institution_ids":["https://openalex.org/I183067930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5148137144"],"corresponding_institution_ids":["https://openalex.org/I183067930"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":10,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.5806000232696533,"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"}},"topics":[{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.5806000232696533,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.18479999899864197,"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":0.08789999783039093,"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/glauber-dynamics","display_name":"Glauber dynamics","score":0.8669999837875366},{"id":"https://openalex.org/keywords/sherrington-kirkpatrick-model","display_name":"Sherrington-Kirkpatrick model","score":0.9850000143051147},{"id":"https://openalex.org/keywords/mixing-time","display_name":"mixing time","score":0.8949999809265137},{"id":"https://openalex.org/keywords/total-variation-distance","display_name":"total variation distance","score":0.7710000276565552},{"id":"https://openalex.org/keywords/poincare-inequality","display_name":"Poincar\u00e9 inequality","score":0.921999990940094},{"id":"https://openalex.org/keywords/logarithmic-sobolev-inequality","display_name":"logarithmic Sobolev inequality","score":0.9269999861717224},{"id":"https://openalex.org/keywords/ising-model","display_name":"Ising model","score":0.890999972820282},{"id":"https://openalex.org/keywords/spin-glass","display_name":"spin glass","score":0.6669999957084656},{"id":"https://openalex.org/keywords/localization-strategy","display_name":"localization strategy","score":0.6729999780654907}],"concepts":[{"id":"https://openalex.org/C2780708879","wikidata":"https://www.wikidata.org/wiki/Q5567254","display_name":"Glauber","level":3,"score":0.8223000168800354},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7247999906539917},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.613099992275238},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.6097999811172485},{"id":"https://openalex.org/C51329190","wikidata":"https://www.wikidata.org/wiki/Q1076349","display_name":"Ising model","level":2,"score":0.517799973487854},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5020999908447266},{"id":"https://openalex.org/C2776085556","wikidata":"https://www.wikidata.org/wiki/Q183361","display_name":"Chen","level":2,"score":0.4966999888420105},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.43560001254081726},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.4341000020503998},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4138000011444092},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3765000104904175},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3131999969482422},{"id":"https://openalex.org/C132878287","wikidata":"https://www.wikidata.org/wiki/Q1671727","display_name":"Inverse Gaussian distribution","level":3,"score":0.30889999866485596},{"id":"https://openalex.org/C2993791989","wikidata":"https://www.wikidata.org/wiki/Q917476","display_name":"Inverse temperature","level":2,"score":0.3050999939441681},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.303600013256073},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.302700012922287},{"id":"https://openalex.org/C42246873","wikidata":"https://www.wikidata.org/wiki/Q6045167","display_name":"Interacting particle system","level":4,"score":0.29910001158714294},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.2924000024795532},{"id":"https://openalex.org/C202213908","wikidata":"https://www.wikidata.org/wiki/Q626011","display_name":"Mean field theory","level":2,"score":0.26440000534057617},{"id":"https://openalex.org/C186394612","wikidata":"https://www.wikidata.org/wiki/Q7098942","display_name":"Optimal design","level":2,"score":0.2556000053882599}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.22159","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.22159","pdf_url":"https://arxiv.org/pdf/2608.22159","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.2608.22159","doi":"https://doi.org/10.48550/arxiv.2608.22159","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.22159","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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.22159","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.22159","pdf_url":"https://arxiv.org/pdf/2608.22159","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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204204510.pdf","grobid_xml":"https://content.openalex.org/works/W7204204510.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W4416948210","https://openalex.org/W4417170716","https://openalex.org/W7160377730","https://openalex.org/W7166562581","https://openalex.org/W7167921910"],"related_works":["https://openalex.org/W3043110366","https://openalex.org/W7212756553","https://openalex.org/W7167921910","https://openalex.org/W7167793785","https://openalex.org/W7222955976","https://openalex.org/W4416948210","https://openalex.org/W7221004152","https://openalex.org/W7095769467","https://openalex.org/W3104870879","https://openalex.org/W7161252711"],"abstract_inverted_index":{"We":[0],"prove":[1],"that":[2],"for":[3,22,69],"every":[4,29],"fixed":[5],"inverse":[6],"temperature":[7],"$\u03b2<":[8],"1":[9],"/":[10,41],"2$,":[11],"with":[12,84],"high":[13],"probability":[14],"over":[15,48],"the":[16,18,23,79,93,102,111,119,122],"disorder,":[17],"single-site":[19],"Glauber":[20],"dynamics":[21],"$n$-spin":[24],"Sherrington-Kirkpatrick":[25],"model":[26],"mixes":[27],"from":[28],"initial":[30],"configuration":[31],"to":[32,56,105],"within":[33],"total":[34],"variation":[35],"distance":[36],"$\\varepsilon$":[37],"in":[38,73],"$O_\u03b2\\left(n":[39],"\\log\\left(n":[40],"\\varepsilon\\right)\\right)$":[42],"steps.":[43],"The":[44,62,115],"bound":[45],"holds":[46],"uniformly":[47],"all":[49],"external":[50],"fields":[51],"and":[52,98],"is":[53,65],"optimal":[54,112],"up":[55],"constants":[57],"depending":[58],"only":[59],"on":[60],"$\u03b2$.":[61],"main":[63,116],"ingredient":[64],"a":[66,85,106],"deterministic":[67],"criterion":[68,82],"optimal-order":[70],"Poincar\u00e9":[71,103,123],"inequalities":[72],"general":[74],"Ising":[75],"models,":[76],"established":[77],"via":[78],"integrated":[80],"Bakry-\u00c9mery":[81],"together":[83],"new":[86],"two-spin":[87],"estimate.":[88],"A":[89],"standard":[90],"application":[91],"of":[92,96,121],"localization-scheme":[94],"framework":[95],"Chen":[97],"Eldan":[99],"then":[100],"upgrades":[101],"inequality":[104,124],"modified":[107],"log-Sobolev":[108],"inequality,":[109],"yielding":[110],"mixing-time":[113],"bound.":[114],"ideas":[117],"underlying":[118],"proof":[120],"were":[125],"generated":[126],"by":[127],"GPT-5.6":[128],"Sol":[129],"Ultra.":[130]},"counts_by_year":[{"year":2026,"cited_by_count":10}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-08-26T00:00:00"}
