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

Yun Long, Asaf Nachmias, Weiyang Ning, Yuval Peres

Research output: Contribution to journalArticlepeer-review

25 Scopus citations

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 languageEnglish
Pages (from-to)i-84
JournalMemoirs of the American Mathematical Society
Volume232
Issue number1092
DOIs
StatePublished - 1 Nov 2014

Keywords

  • Ising model
  • Markov chains
  • Mixing time
  • Swendsen-Wang algorithm

Fingerprint

Dive into the research topics of 'A power law of order 1/4 for critical mean field Swendsen-Wang dynamics'. Together they form a unique fingerprint.

Cite this