Invasion percolation: new algorithms and universality classes

Employing highly efficient algorithms for simulating invasion percolation ( IP), whose execution time scales as O[M log (M)] or better for a cluster of M sites, and for determining the backbone of the cluster, we obtain precis e estimates for the fractal dimensions of the sample-spanning cluster, the backbone, and the minimal path in order to identify the universality classe s of four different IP processes (site and bond IP with and without trappin g). In two dimensions IP is characterized by two universality classes, one each for LP without trapping, and site and bond IP with trapping. In a thre e-dimensional site IP with and without trapping is in the universality clas s of random percolation, while bond IP with trapping is in a distinct unive rsality class, which may be the same as that of optimal paths in strongly d isordered media.