Effects of flipping rules in cluster algorithms

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Abstract
Studying rules for flipping cluster spins, one with the fastest decay of autocorrelations is found. It turns out that connectivity of clusters is an additional crucial parameter. Another result is that there are only a few eigenvalues of the transition matrix which play a role. One eigenvalue dominates if the flipped cluster distribution is extended. The lattice size dependence of the weights of the eigenvalues is observed for the first time.