文章基本信息

标题：Glauber Dynamics for Ising Model on Convergent Dense Graph Sequences
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作者：Rupam Acharyya ; Daniel Stefankovic
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2017
卷号：81
页码：23:1-23:22
DOI：10.4230/LIPIcs.APPROX-RANDOM.2017.23
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We study the Glauber dynamics for Ising model on (sequences of) dense graphs. We view the dense graphs through the lens of graphons. For the ferromagnetic Ising model with inverse temperature beta on a convergent sequence of graphs G_n with limit graphon W we show fast mixing of the Glauber dynamics if beta * lambda_1(W) 1 (where lambda_1(W)is the largest eigenvalue of the graphon). We also show that in the case beta * lambda_1(W) = 1 there is insufficient information to determine the mixing time (it can be either fast or slow).
关键词：Spin systems; Glauber dynamics; Ising model; graphons