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We compare the correlation times of the Sweeny and Gliozzi dynamics fortwo-dimensional Ising and three-state Potts models, and the three-dimensionalIsing model for the simulations in the percolation prepresentation. The resultsare also compared with Swendsen-Wang and Wolff cluster dynamics. It is foundthat Sweeny and Gliozzi dynamics have essentially the same dynamical criticalbehavior. Contrary to Gliozzi's claim (cond-mat/0201285), the Gliozzi dynamicshas critical slowing down comparable to that of other cluster methods. For thetwo-dimensional Ising model, both Sweeny and Gliozzi dynamics give good fits tologarithmic size dependences; for two-dimensional three-state Potts model,their dynamical critical exponent z is 0.49(1); the three-dimensional Isingmodel has z = 0.37(2).Comment: RevTeX, 4 pages, 5 figure

Sweeny and Gliozzi dynamics for simulations of Potts models in the Fortuin-Kasteleyn representation