Comparison of Swendsen-Wang and Heat-Bath Dynamics

Abstract

We prove that the spectral gap of the Swendsen-Wang process for the Potts model on graphs with bounded degree is bounded from below by some constant times the spectral gap of any single-spin dynamics. This implies rapid mixing of the Swendsen-Wang process for the two-dimensional Potts model at all temperatures above the critical one, as well as rapid mixing at the critical temperature for the Ising model. After this we introduce a modified version of the Swendsen-Wang algorithm for planar graphs and prove rapid mixing for the two-dimensional Potts models at all non-critical temperatures.

22 pages, 1 figure

References in corpus (1)

• On the mixing time of the 2D stochastic Ising model with "plus" boundary conditions at low temperature

Cited by in corpus (3)

• Swendsen-Wang is faster than single-bond dynamics
• The worm process for the Ising model is rapidly mixing
• Random-cluster dynamics on random regular graphs in tree uniqueness