Abstract
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(√n) for all non-critical temperatures. In this paper we show that the mixing time is θ(1) in high temperatures, θ(log n) in low temperatures and θ(n1/4) at criticality. We 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.
Original language | English |
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Pages (from-to) | i-84 |
Journal | Memoirs of the American Mathematical Society |
Volume | 232 |
Issue number | 1092 |
DOIs | |
State | Published - 1 Nov 2014 |
Keywords
- Ising model
- Markov chains
- Mixing time
- Swendsen-Wang algorithm