Fixed-cluster acceleration algorithm for spin systems

A recently introduced cluster acceleration algorithm for spin models [J. Machta et al., Phys. Rev. Lett. 75 2792 (1995)] based on invasion percolation is generalized to temperatures away from the critical point using concepts of random bond percolation. The generalized algorithm is equivalent to an "optimized" version of the Swendsen-Wang cluster algorithm [R. H. Swendsen and J. S. Wang, Phys. Rev. Lett. 58 86 (1987)], and we demonstrate its success and speed at all temperatures for the d=2 Ising model. We argue that the previously discussed connection to self-organized criticality may be viewed as one limit of the fixed-cluster algorithm.