Comparison of cluster algorithms for two-dimensional Potts models.

We have measured the dynamical critical exponent {ital z} for the Swendsen-Wang and the Wolff cluster update algorithms, as well as a number of variants of these algorithms, for the {ital q}=2 and {ital q}=3 Potts models in two dimensions. We find that although the autocorrelation times differ considerably between algorithms, the critical exponents are the same. For {ital q}=2, we find that although the data are better fitted by a logarithmic increase in the autocorrelation time with lattice size, they are also consistent with a power law with exponent {ital z}{approx}0.25, especially if there are non-negligible corrections to scaling.