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Simulations of the two-dimensional Ising and 3-state Potts models at their critical points are performed using the invaded cluster (IC) algorithm. It is argued that observables measured on a sub-lattice 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 τε(l, L) for an l × l sub-lattice attains a maximum in the crossover region, and a dynamic exponent z IC for the IC algorithm is defined according to τε,max ∼ L z IC . Simulation results for the 3-state model yield z IC = .346 ± .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 < .21 and possibly that τε,max ∼ log L so that z IC = 0-similar to previous results for the SW and Wolff algorithms.

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