Journal of Statistical Physics, Vol. 90, Nos. 5/6, 1998, p. 1277-1293.
We investigate the dynamical behavior of the recently proposed multibondic cluster Monte Carlo algorithm in applications to the three-dimensional q-state Potts models with q = 3, 4, and 5 in the vicinity of their first-order phase transition points. For comparison we also report simulations with the standard multi-canonical algorithm. Similar to the findings in two dimensions, we show that for the multibondic cluster algorithm the dependence of the autocorrelation time t on the system size V is well described by the power law t V^alpha and that the dynamical exponent a is consistent with the optimal random walk estimate alpha = I. For the multicanonical simulations we obtain, as expected, a larger value of alpha = 1.2.