Cutoff for the Swendsen-wang dynamics on the lattice

Danny Nam, Allan Sly

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We study the Swendsen-Wang dynamics for the q-state Potts model on the lattice. Introduced as an alternative algorithm of the classical singlesite Glauber dynamics, the Swendsen-Wang dynamics is a nonlocal Markov chain that recolors many vertices at once based on the random-cluster representation of the Potts model. In this work, we establish cutoff phenomenon for the Swendsen-Wang dynamics on the lattice at sufficiently high temperatures, proving that it exhibits a sharp transition from "unmixed" to "well mixed." In particular, we show that at high enough temperatures the Swendsen-Wang dynamics on the torus (Z/nZ)d has cutoff at time (-log(1-γ)-1 log n, where γ (β) is the spectral gap of the infinitevolume dynamics.

Original languageEnglish (US)
Pages (from-to)3705-3761
Number of pages57
JournalAnnals of Probability
Issue number6
StatePublished - 2019

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Cutoff phenomenon
  • Markov chains
  • Potts model
  • Swendsen-Wang dynamics


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