When you look at the original paper of Swendsen and Wang in 1987: "Nonuniversal critical dynamics in Monte Carlo simulations" it is somewhat mentioned that the proposed algorithm uses percolation theory and the autocorrelation time is significantly reduced:
In this paper, we present an unusal type of dynamics, which violates dynamic universality, and greatly reduces relaxation times in the computer simulation of large systems. Large clusters are changed in a single move, so that the profcess is not local in the usual sense, allowing z to be less than the lower bound...
After proving the necessary condition of detailed balance, they spread some words about the origin of this behavior,
The percolation clusters behave as Fisher droplets and contain a great deal of information".
but only from the publication I cannot understand why this is working. I followed some sources, but obviously not the right one.
My question: Can someone outline how percolation theory comes into play? That the algorithm is working due to the detailed balance condition is not a surprise, but that its autocorrelation time is reduced like this seems curious to me.
the next question would be: What are the main differences between the Wolff and the Swendsen-Wang algorithm? As far as I see it Wolff uses a good choice of the probability so that there are no rejections, is this true?