A power law of order 1/4 for critical mean field Swendsen-Wang dynamics

A power law of order 1/4 for critical mean field Swendsen-Wang dynamics / Yun Long, Asaf Nachmias, Weiyang Ning, Yuval Peres.

The Swendsen-Wang dynamics is a Markov chain widely used by physicists to sample from the Boltzmann-Gibbs distribution of the Ising model. Cooper, Dyer, Frieze and Rue proved that on the complete graph K_n the mixing time of the chain is at most O(\sqrt{n}) for all non-critical temperatures. In this...

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Bibliographic Details
Main Authors: Long, Yun, 1982- (Author), Nachmias, Asaf (Author), Ning, Weiyang (Author), Peres, Y. (Yuval) (Author)
Format: eBook
Language:English
Published: Providence, Rhode Island : American Mathematical Society, 2014.
Series:Memoirs of the American Mathematical Society ; no. 1092.
Subjects:
Markov processes.
Spin waves > Mathematical models.
Markov processes
Spin waves > Mathematical models
Online Access:Click for online access
Description
Summary:The Swendsen-Wang dynamics is a Markov chain widely used by physicists to sample from the Boltzmann-Gibbs distribution of the Ising model. Cooper, Dyer, Frieze and Rue proved that on the complete graph K_n the mixing time of the chain is at most O(\sqrt{n}) for all non-critical temperatures. In this paper the authors show that the mixing time is \Theta(1) in high temperatures, \Theta(\log n) in low temperatures and \Theta(n^{1/4}) at criticality. They also provide an upper bound of O(\log n) for Swendsen-Wang dynamics for the q-state ferromagnetic Potts model on any tree of n vertices.
Item Description:"Volume 232, Number 1092 (fourth of 6 numbers), November 2014."
Physical Description:1 online resource (v, 84 pages)
Bibliography:Includes bibliographical references (pages 83-84).
ISBN:9781470418953
1470418959
ISSN:0065-9266 ;
Language:English.
Source of Description, Etc. Note:Print version record.

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