{"id":"https://openalex.org/W7123306756","doi":"https://doi.org/10.1103/5ypm-x96s","title":"Slow mixing and emergent one-form symmetries in three-dimensional Z 2 gauge theory","display_name":"Slow mixing and emergent one-form symmetries in three-dimensional Z 2 gauge theory","publication_year":2026,"publication_date":"2026-08-26","ids":{"openalex":"https://openalex.org/W7123306756","doi":"https://doi.org/10.1103/5ypm-x96s","pmid":"https://pubmed.ncbi.nlm.nih.gov/42888800"},"language":"en","primary_location":{"id":"doi:10.1103/5ypm-x96s","doi":"https://doi.org/10.1103/5ypm-x96s","is_oa":false,"landing_page_url":"https://doi.org/10.1103/5ypm-x96s","pdf_url":null,"source":{"id":"https://openalex.org/S4210235286","display_name":"Physical review. E","issn_l":"2470-0045","issn":["2470-0045","2470-0053","2470-0061"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","ki-jl-1","medline","norway-1","poland-140","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 E","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2601.06010","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015510724","display_name":"Charles Stahl","orcid":"https://orcid.org/0000-0002-9809-5575","observed_orcids":["https://orcid.org/0000-0002-9809-5575"]},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Charles Stahl","raw_affiliation_strings":["Stanford University"],"raw_orcid":"https://orcid.org/0000-0002-9809-5575","affiliations":[{"raw_affiliation_string":"Stanford University","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014641750","display_name":"Benedikt Placke","orcid":"https://orcid.org/0000-0002-9975-7120","observed_orcids":["https://orcid.org/0000-0002-9975-7120"]},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Benedikt Placke","raw_affiliation_strings":["University of Oxford"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Oxford","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071769814","display_name":"Vedika Khemani","orcid":"https://orcid.org/0000-0003-2653-0555","observed_orcids":["https://orcid.org/0000-0003-2653-0555","https://orcid.org/0000-0003-2874-117X"]},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Vedika Khemani","raw_affiliation_strings":["Stanford University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Stanford University","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5122825963","display_name":"Yaodong Li","orcid":"https://orcid.org/0000-0003-3742-1944","observed_orcids":["https://orcid.org/0000-0003-3742-1944"]},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]},{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yaodong Li","raw_affiliation_strings":["Department of Mechanical Engineering and Department of Physics, University of Washington, Seattle, Washington 98195, USA","Stanford University"],"raw_orcid":"https://orcid.org/0000-0003-3742-1944","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering and Department of Physics, University of Washington, Seattle, Washington 98195, USA","institution_ids":["https://openalex.org/I201448701"]},{"raw_affiliation_string":"Stanford University","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05873352,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"114","issue":"3","first_page":"034126","last_page":"034126"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11804","display_name":"Quantum many-body systems","score":0.70169997215271,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T11804","display_name":"Quantum many-body systems","score":0.70169997215271,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T10591","display_name":"Theoretical and Computational Physics","score":0.21899999678134918,"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/T11682","display_name":"Advanced Condensed Matter Physics","score":0.019200000911951065,"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/slow-mixing","display_name":"slow mixing","score":0.5669999718666077},{"id":"https://openalex.org/keywords/mixing-time","display_name":"mixing time","score":0.6629999876022339},{"id":"https://openalex.org/keywords/1-form-symmetry","display_name":"1-form symmetry","score":0.8479999899864197},{"id":"https://openalex.org/keywords/emergent-symmetry","display_name":"emergent symmetry","score":0.800000011920929},{"id":"https://openalex.org/keywords/z2-lattice-gauge-theory","display_name":"Z2 lattice gauge theory","score":0.8970000147819519},{"id":"https://openalex.org/keywords/deconfined-phase","display_name":"deconfinement phase","score":0.8190000057220459},{"id":"https://openalex.org/keywords/activation-barrier","display_name":"activation barrier","score":0.8289999961853027},{"id":"https://openalex.org/keywords/entropic-effects","display_name":"entropic effects","score":0.8309999704360962},{"id":"https://openalex.org/keywords/memory","display_name":"memory","score":0.4059999883174896},{"id":"https://openalex.org/keywords/confinement-transition","display_name":"confinement transition","score":0.9879999756813049},{"id":"https://openalex.org/keywords/dynamic-scaling","display_name":"dynamic scaling","score":0.734000027179718},{"id":"https://openalex.org/keywords/self-correcting-quantum-memory","display_name":"self-correcting quantum memory","score":0.7609999775886536},{"id":"https://openalex.org/keywords/3d-ising-model","display_name":"three-dimensional Ising model","score":0.7070000171661377}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.7253999710083008},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.6592000126838684},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.5002999901771545},{"id":"https://openalex.org/C51329190","wikidata":"https://www.wikidata.org/wiki/Q1076349","display_name":"Ising model","level":2,"score":0.48660001158714294},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4733000099658966},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.4700999855995178},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.4577000141143799},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4171999990940094},{"id":"https://openalex.org/C174256460","wikidata":"https://www.wikidata.org/wiki/Q911364","display_name":"Perturbation theory (quantum mechanics)","level":2,"score":0.38199999928474426},{"id":"https://openalex.org/C181830111","wikidata":"https://www.wikidata.org/wiki/Q214850","display_name":"Gauge theory","level":2,"score":0.38029998540878296},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.37880000472068787},{"id":"https://openalex.org/C204795200","wikidata":"https://www.wikidata.org/wiki/Q903282","display_name":"Symmetry breaking","level":2,"score":0.34470000863075256},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.3443000018596649},{"id":"https://openalex.org/C125881977","wikidata":"https://www.wikidata.org/wiki/Q736716","display_name":"Spontaneous symmetry breaking","level":3,"score":0.3425999879837036},{"id":"https://openalex.org/C180188523","wikidata":"https://www.wikidata.org/wiki/Q574576","display_name":"Exponential decay","level":2,"score":0.33959999680519104},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.3353999853134155},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.3343999981880188},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.31290000677108765},{"id":"https://openalex.org/C194807282","wikidata":"https://www.wikidata.org/wiki/Q900634","display_name":"Critical phenomena","level":3,"score":0.31049999594688416},{"id":"https://openalex.org/C158129726","wikidata":"https://www.wikidata.org/wiki/Q402","display_name":"Higgs boson","level":2,"score":0.3068000078201294},{"id":"https://openalex.org/C104416048","wikidata":"https://www.wikidata.org/wiki/Q302518","display_name":"Propagator","level":2,"score":0.28790000081062317},{"id":"https://openalex.org/C149288129","wikidata":"https://www.wikidata.org/wiki/Q185357","display_name":"Phase transition","level":2,"score":0.2858999967575073},{"id":"https://openalex.org/C2778242569","wikidata":"https://www.wikidata.org/wiki/Q1996344","display_name":"Continuous symmetry","level":2,"score":0.27959999442100525},{"id":"https://openalex.org/C164154869","wikidata":"https://www.wikidata.org/wiki/Q901927","display_name":"Critical exponent","level":3,"score":0.2759999930858612},{"id":"https://openalex.org/C99874945","wikidata":"https://www.wikidata.org/wiki/Q188715","display_name":"Statistical mechanics","level":2,"score":0.2754000127315521},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.26899999380111694},{"id":"https://openalex.org/C147247565","wikidata":"https://www.wikidata.org/wiki/Q5527635","display_name":"Gauge symmetry","level":3,"score":0.2687000036239624},{"id":"https://openalex.org/C174084160","wikidata":"https://www.wikidata.org/wiki/Q908049","display_name":"Bound state","level":2,"score":0.2646999955177307},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.25769999623298645},{"id":"https://openalex.org/C141886431","wikidata":"https://www.wikidata.org/wiki/Q1193821","display_name":"Quantum fluctuation","level":3,"score":0.25619998574256897},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.2558000087738037}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1103/5ypm-x96s","doi":"https://doi.org/10.1103/5ypm-x96s","is_oa":false,"landing_page_url":"https://doi.org/10.1103/5ypm-x96s","pdf_url":null,"source":{"id":"https://openalex.org/S4210235286","display_name":"Physical review. E","issn_l":"2470-0045","issn":["2470-0045","2470-0053","2470-0061"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","ki-jl-1","medline","norway-1","poland-140","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 E","raw_type":"journal-article"},{"id":"pmid:42888800","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/42888800","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. E","raw_type":"Journal Article"},{"id":"pmh:oai:arXiv.org:2601.06010","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2601.06010","pdf_url":"https://arxiv.org/pdf/2601.06010","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2601.06010","doi":"https://doi.org/10.48550/arxiv.2601.06010","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.06010","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2601.06010","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2601.06010","pdf_url":"https://arxiv.org/pdf/2601.06010","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1625084116","display_name":"Emergent Phenomena in Quantum Systems Theory Center","funder_award_id":"GBMF8686","funder_id":"https://openalex.org/F4320306202","funder_display_name":"Gordon and Betty Moore Foundation"},{"id":"https://openalex.org/G3398237449","display_name":null,"funder_award_id":"PHY-2309135","funder_id":"https://openalex.org/F4320337427","funder_display_name":"Kavli Institute for Theoretical Physics, University of California, Santa Barbara"},{"id":"https://openalex.org/G4486752075","display_name":null,"funder_award_id":"N00014-24-1-2098","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G4689434848","display_name":null,"funder_award_id":"2309135","funder_id":"https://openalex.org/F4320337427","funder_display_name":"Kavli Institute for Theoretical Physics, University of California, Santa Barbara"},{"id":"https://openalex.org/G5356677024","display_name":null,"funder_award_id":"PHY-2309135","funder_id":"https://openalex.org/F4320306202","funder_display_name":"Gordon and Betty Moore Foundation"},{"id":"https://openalex.org/G6306315162","display_name":"THE GEOMETRY AND FLOW OF QUANTUM INFORMATION: FROM QUANTUM GRAVITY TO QUANTUM TECHNOLOGY","funder_award_id":"DESC0019380","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G7002119356","display_name":"Kavli Institute for Theoretical Physics","funder_award_id":"2309135","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306079","display_name":"David and Lucile Packard Foundation","ror":"https://ror.org/032atxq54"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320306202","display_name":"Gordon and Betty Moore Foundation","ror":"https://ror.org/006wxqw41"},{"id":"https://openalex.org/F4320308269","display_name":"Alexander von Humboldt-Stiftung","ror":"https://ror.org/012kf4317"},{"id":"https://openalex.org/F4320319993","display_name":"Leverhulme Trust","ror":"https://ror.org/012mzw131"},{"id":"https://openalex.org/F4320320290","display_name":"University of Oxford","ror":"https://ror.org/052gg0110"},{"id":"https://openalex.org/F4320332359","display_name":"Office of Science","ror":"https://ror.org/00mmn6b08"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"},{"id":"https://openalex.org/F4320337427","display_name":"Kavli Institute for Theoretical Physics, University of California, Santa Barbara","ror":"https://ror.org/02t274463"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7123306756.pdf","grobid_xml":"https://content.openalex.org/works/W7123306756.grobid-xml"},"referenced_works_count":66,"referenced_works":["https://openalex.org/W287535836","https://openalex.org/W1577101430","https://openalex.org/W1631650672","https://openalex.org/W1972090289","https://openalex.org/W1979388055","https://openalex.org/W1980496924","https://openalex.org/W1986155946","https://openalex.org/W1994642941","https://openalex.org/W1995714262","https://openalex.org/W2001353470","https://openalex.org/W2003341284","https://openalex.org/W2008217797","https://openalex.org/W2009386142","https://openalex.org/W2009989296","https://openalex.org/W2012901551","https://openalex.org/W2013345719","https://openalex.org/W2023883372","https://openalex.org/W2024718670","https://openalex.org/W2026034750","https://openalex.org/W2028422873","https://openalex.org/W2029387475","https://openalex.org/W2065035260","https://openalex.org/W2066359652","https://openalex.org/W2072211488","https://openalex.org/W2073598303","https://openalex.org/W2078944931","https://openalex.org/W2079416076","https://openalex.org/W2083178078","https://openalex.org/W2085266415","https://openalex.org/W2088636071","https://openalex.org/W2124148162","https://openalex.org/W2125986857","https://openalex.org/W2132142633","https://openalex.org/W2135902788","https://openalex.org/W2136497493","https://openalex.org/W2136565179","https://openalex.org/W2159566537","https://openalex.org/W2169919279","https://openalex.org/W2223222229","https://openalex.org/W2263744690","https://openalex.org/W2308177793","https://openalex.org/W2765846489","https://openalex.org/W2767566909","https://openalex.org/W2885549115","https://openalex.org/W2901200300","https://openalex.org/W2912187847","https://openalex.org/W3000046675","https://openalex.org/W3001911293","https://openalex.org/W3006749615","https://openalex.org/W3037698542","https://openalex.org/W3141849522","https://openalex.org/W3207431311","https://openalex.org/W4229532324","https://openalex.org/W4233055081","https://openalex.org/W4306952031","https://openalex.org/W4389046682","https://openalex.org/W4394875044","https://openalex.org/W4402206846","https://openalex.org/W4406868492","https://openalex.org/W4408330763","https://openalex.org/W4410019762","https://openalex.org/W4411933381","https://openalex.org/W4411955144","https://openalex.org/W4415975696","https://openalex.org/W7160940053","https://openalex.org/W7166571717"],"related_works":["https://openalex.org/W7123371135","https://openalex.org/W3186267132","https://openalex.org/W2663254750","https://openalex.org/W4410019762","https://openalex.org/W3114672933","https://openalex.org/W1671488553","https://openalex.org/W4416663963","https://openalex.org/W7051973998","https://openalex.org/W4406603938","https://openalex.org/W2006381579"],"abstract_inverted_index":{"Symmetry-breaking":[0],"order":[1],"at":[2,129,186],"low":[3],"temperatures":[4],"is":[5,42,84],"often":[6],"accompanied":[7],"by":[8,182],"slow":[9],"relaxation":[10,52],"dynamics,":[11],"due":[12],"to":[13,29,125,150,201,230],"diverging":[14,126],"free-energy":[15,127],"barriers":[16,113,128],"arising":[17],"from":[18,170],"interfaces":[19,46],"between":[20,47,104,114],"different":[21,105,204],"ordered":[22,35,115],"states.":[23,107],"Here":[24],"we":[25,118,159],"extend":[26],"this":[27,180,222],"correspondence":[28],"classical":[30,58,141],"topological":[31],"order,":[32],"where":[33,82],"the":[34,51,55,74,78,85,94,101,111,135,165,174,187,194,211,216],"states":[36],"are":[37,199],"locally":[38],"indistinguishable,":[39],"so":[40],"there":[41],"no":[43],"notion":[44,157],"of":[45,54,96,173,193,215],"them.":[48],"We":[49,68,143,162,220],"study":[50],"dynamics":[53],"three-dimensional":[56],"(3D)":[57],"Z_{2}":[59],"lattice":[60],"gauge":[61],"theory":[62],"(LGT)":[63],"as":[64,137],"a":[65,70,138,156],"canonical":[66],"example.":[67],"prove":[69,145],"lower":[71],"bound":[72,90],"on":[73],"mixing":[75,167,184],"time":[76,168],"in":[77,93],"deconfined":[79,175,195],"phase,":[80,176],"t_{mix}=exp[\u03a9(L)],":[81],"L":[83],"linear":[86],"system":[87],"size.":[88],"This":[89,108],"applies":[91],"even":[92,207],"presence":[95],"perturbations":[97],"that":[98,120,146,158,164],"explicitly":[99],"break":[100],"one-form":[102,153],"symmetry":[103,229],"long-lived":[106],"perturbation":[109],"destroys":[110],"energy":[112],"states,":[116],"but":[117],"show":[119],"entropic":[121,147,223],"effects":[122,148],"nevertheless":[123],"lead":[124,149],"nonzero":[130],"temperature.":[131],"Our":[132],"proof":[133],"establishes":[134],"LGT":[136],"robust":[139],"finite-temperature":[140],"memory.":[142],"further":[144],"an":[151],"emergent":[152,228],"symmetry,":[154],"via":[155],"make":[160],"precise.":[161],"argue":[163],"exponential":[166],"follows":[169],"universal":[171],"properties":[172],"and":[177,189,227],"numerically":[178],"corroborate":[179],"expectation":[181],"exploring":[183],"timescales":[185],"Higgs":[188],"confinement":[190],"transitions":[191,198],"out":[192],"phase.":[196],"These":[197],"found":[200],"exhibit":[202],"markedly":[203],"dynamic":[205],"scaling,":[206],"though":[208],"both":[209],"have":[210],"static":[212],"critical":[213],"exponents":[214],"3D":[217],"Ising":[218],"model.":[219],"expect":[221],"mechanism":[224],"for":[225],"memory":[226],"also":[231],"bring":[232],"insight":[233],"into":[234],"self-correcting":[235],"quantum":[236],"memories.":[237]},"counts_by_year":[],"updated_date":"2026-10-31T12:09:11.096373","created_date":"2026-01-13T00:00:00"}
