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A Power Law of Order 1/4 for Critical Mean Field Swendsen-Wang Dynamics

Yuval Peres author Yun Long author Asaf Nachmias author Weiyang Ning author

Format:Paperback

Publisher:American Mathematical Society

Published:30th Oct '14

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A Power Law of Order 1/4 for Critical Mean Field Swendsen-Wang Dynamics cover

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 Kn the mixing time of the chain is at most O(Ön) for all non-critical temperatures.

In this paper the authors show that the mixing time is Q(1) in high temperatures, Q(log n) in low temperatures and Q(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.

ISBN: 9781470409104

Dimensions: unknown

Weight: 300g

84 pages