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Mixing of the Glauber dynamics for the ferromagnetic Potts model.

Bordewich, Magnus and Greenhill, Catherine and Patel, Viresh (2016) 'Mixing of the Glauber dynamics for the ferromagnetic Potts model.', Random structures and algorithms., 48 (1). pp. 21-52.

Abstract

We present several results on the mixing time of the Glauber dynamics for sampling from the Gibbs distribution in the ferromagnetic Potts model. At a fixed temperature and interaction strength, we study the interplay between the maximum degree (Δ) of the underlying graph and the number of colours or spins (q) in determining whether the dynamics mixes rapidly or not. We find a lower bound L on the number of colours such that Glauber dynamics is rapidly mixing if at least L colours are used. We give a closely-matching upper bound U on the number of colours such that with probability that tends to 1, the Glauber dynamics mixes slowly on random Δ-regular graphs when at most U colours are used. We show that our bounds can be improved if we restrict attention to certain types of graphs of maximum degree Δ, e.g. toroidal grids for Δ = 4.

Item Type:Article
Keywords:Glauber dynamics, Mixing time, Potts model, Ferromagnetic.
Full text:(VoR) Version of Record
Available under License - Creative Commons Attribution.
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Full text:(VoR) Version of Record
Available under License - Creative Commons Attribution.
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Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1002/rsa.20569
Publisher statement:© 2015 The Authors Random Structures & Algorithms Published by Wiley Periodicals, Inc. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Date accepted:14 April 2014
Date deposited:23 September 2015
Date of first online publication:04 September 2014
Date first made open access:No date available

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