Mean Field Behavior of Cluster Dynamics
  The dynamic behavior of cluster algorithms is analyzed in the classical mean field limit. Rigorous analytical results below $T_c$ establish that the dynamic exponent has the value $z_{sw}=1$ for the Swendsen-Wang algorithm and $z_{uw}=0$ for the Wolff algorithm.   An efficient Monte Carlo implementation is introduced, adapted for using these algorithms for fully connected graphs. Extensive simulations both above and below $T_c$ demonstrate scaling and evaluate the finite-size scaling function by means of a rather impressive collapse of the data. 
N. Persky, R. Ben-Av, I. Kanter and E. Domany