Dynamic and static properties of the invaded cluster algorithm

Simulations of the two-dimensional Ising and three-state Potts models at their critical points are performed using the invaded cluster ~IC! algorithm. It is argued that observables measured on a sublattice of size l should exhibit a crossover to Swendsen-Wang ~SW! behavior for l sufficiently less than the lattice size L, and a scaling form is proposed to describe the crossover phenomenon. It is found that the energy autocorrelation time t «(l,L) for an l3l sublattice attains a maximum in the crossover region, and a dynamic exponent z IC for the IC algorithm is defined according to t «,max;L z IC . Simulation results for the three-state model yield z IC 50.34660.002, which is smaller than values of the dynamic exponent found for the SW and Wolff algorithms and also less than the Li-Sokal bound. The results are less conclusive for the Ising model, but it appears that z IC ,0.21 and possibly that t «,max;ln L so that z IC 50—similar to previous results for the SW and Wolff algorithms. @S1063-651X~99!00902-2#