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(OEn) 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.
- ISBN13 9781470409104
- Publish Date 30 October 2014
- Publish Status Active
- Publish Country US
- Imprint American Mathematical Society
- Format Paperback
- Pages 84
- Language English