2026-10-09T02:33:11Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:7572 2024-03-06T09:40:38Z ddc:004 open_access

Glauber Dynamics for Ising Model on Convergent Dense Graph Sequences Acharyya, Rupam Stefankovic, Daniel Spin systems Glauber dynamics Ising model graphons 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$ and slow (torpid) mixing 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). Schloss Dagstuhl – Leibniz-Zentrum für Informatik Rupam Acharyya and Daniel Stefankovic 2017 Is Part Of LIPIcs, Volume 81, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.APPROX-RANDOM.2017.23 urn:nbn:de:0030-drops-75724 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2017.23 eng https://creativecommons.org/licenses/by/3.0/legalcode