A Power Law of Order 1/4 for Critical Mean Field Swendsen-Wang Dynamics |
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| Author:
| Long, Yun
Nachmias, Asaf
Ning, Weiyang
Peres, Yuval |
| Series title: | Memoirs of the American Mathematical Society Ser. |
| ISBN: | 978-1-4704-0910-4 |
| Publication Date: | Oct 2014 |
| Publisher: | American Mathematical Society
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| Book Format: | Paperback |
| List Price: | USD $69.00USD $69.00 |
Book Description:
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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( Ö n) 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.
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( Ö n) 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.