Mean-field behavior of cluster dynamics.

The dynamic behavior of cluster algorithms is analyzed in the classical mean-field limit. Rigorous analytical results below ${\mathit{T}}_{\mathit{c}}$ establish that the dynamic exponent has the value ${\mathit{z}}_{\mathrm{SW}}$=1 for the Swendsen-Wang algorithm and ${\mathit{z}}_{\mathit{W}}$=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 ${\mathit{T}}_{\mathit{c}}$ demonstrate scaling and evaluate the finite-size scaling function by means of a rather impressive collapse of the data. \textcopyright{} 1996 The American Physical Society.