Efficient cluster algorithms for Ising systems with fields are described. Cluster are grown between two replicas of the system in the same field. As is the case for other successful cluster approaches, the critical point of the spin system coincides with the percolation threshold of the clusters. Applications are discussed.
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.