Torpid Mixing of Some Monte Carlo Markov Chain Algorithms in Statistical Physics

We study two widely used algorithms, Glauber dynamics and the Swendsen-Wang algorithm, on rectangular subsets of the hypercubic lattice Zd. We prove that under certain circumstances, the mixing time in a box of side length L with periodic boundary conditions can be exponential in Ld-1. In other words, under these circumstances, the mixing...更多