{"id":357857,"date":"2017-01-25T14:15:59","date_gmt":"2017-01-25T22:15:59","guid":{"rendered":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/?post_type=msr-research-item&p=357857"},"modified":"2018-10-16T20:01:35","modified_gmt":"2018-10-17T03:01:35","slug":"mixing-time-ising-model-uniform-lower-bound-graphs","status":"publish","type":"msr-research-item","link":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/publication\/mixing-time-ising-model-uniform-lower-bound-graphs\/","title":{"rendered":"Mixing Time For The Ising Model: A Uniform Lower Bound For All Graphs"},"content":{"rendered":"

Consider Glauber dynamics for the Ising model on a graph of n<\/span><\/span><\/span><\/span> vertices. Hayes and Sinclair showed that the mixing time for this dynamics is at least n<\/span>log<\/span><\/span>n<\/span>\/<\/span><\/span><\/span>f<\/span>(<\/span>\u0394<\/span>)<\/span><\/span><\/span><\/span>, where \u0394<\/span><\/span><\/span><\/span> is the maximum degree and f<\/span>(<\/span>\u0394<\/span>)<\/span>=<\/span>\u0398<\/span>(<\/span>\u0394<\/span>log<\/span>2<\/span><\/span><\/span>\u0394<\/span>)<\/span><\/span><\/span><\/span>. Their result applies to more general spin systems, and in that generality, they showed that some dependence on \u0394<\/span><\/span><\/span><\/span> is necessary. In this paper, we focus on the ferromagnetic Ising model and prove that the mixing time of Glauber dynamics on any n<\/span><\/span><\/span><\/span>-vertex graph is at least (<\/span>1<\/span>\/<\/span><\/span><\/span>4<\/span>+<\/span>o<\/span>(<\/span>1<\/span>)<\/span>)<\/span>n<\/span>log<\/span><\/span>n<\/span><\/span><\/span><\/span>.<\/p>\n","protected":false},"excerpt":{"rendered":"

Consider Glauber dynamics for the Ising model on a graph of n vertices. Hayes and Sinclair showed that the mixing time for this dynamics is at least nlogn\/f(\u0394), where \u0394 is the maximum degree and f(\u0394)=\u0398(\u0394log2\u0394). Their result applies to more general spin systems, and in that generality, they showed that some dependence on \u0394 […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"Institut Henri Poincar\u00c3\u00a9","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"Annales de l'Institut Henri Poincar\u00c3\u00a9, Probabilit\u00c3\u00a9s et 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