Before revision: The Swendsen-Wang algorithm is a sophisticated, widely-used Markov chain for sampling from the Gibbs distribution for the ferromagnetic Ising and Potts models with inverse temperature \beta>0. Due to the global nature of the updatesof the Swendsen-Wang algorithm, the underlying Markov chain often mixes rapidly in the low temperature region (large \beta) where long-range correlations impair the convergence rate of local chains such as the Glauber dynamics.
After revision: The Swendsen-Wang algorithm is a sophisticated, widely-used Markov chain for sampling from the Gibbs distribution for the ferromagnetic Ising and Potts models . This chain has proved difficult to analyze, due in part to the global nature of the updatesof the Swendsen-Wang algorithm, the underlying Markov chain often mixes rapidly in the low temperature region (large \beta) where long-range correlations impair the convergence rate of local chains such as the Glauber dynamics.