Improved Rosenbluth Monte Carlo scheme for cluster counting and lattice animal enumeration

We describe an algorithm for the Rosenbluth Monte Carlo enumeration of clus ters and lattice animals. The method may also be used to calculate associat ed properties such as moments or perimeter multiplicities of the clusters. The scheme is an extension of the Rosenbluth method for growing polymer cha ins and is a simplification of a scheme reported earlier by one of the auth ors. The algorithm may be used to obtain a Monte Carlo estimate of the numb er of distinct lattice animals on any lattice topology. The method is valid ated against exact and Monte Carlo enumerations for clusters up to size 50, on a two dimensional square lattice and three dimensional simple cubic lat tice. The method may be readily adapted to yield Boltzmann weighted average s over clusters.