An improved Rosenbluth Monte Carlo scheme for cluster counting and lattice animal enumeration

Abstract

We describe an algorithm for the Rosenbluth Monte Carlo enumeration of clusters and lattice animals. The method may also be used to calculate associated properties such as moments or perimeter multiplicities of the clusters. The new scheme is an extension of the Rosenbluth method for growing polymer chains and is a simplification of a scheme reported earlier by one of the authors. The algorithm may be used to estimate the number of distinct lattice animals on any lattice topology. The method is validated against exact and Monte Carlo enumerations for clusters up to size 50, on a two dimensional square lattice and three dimensional simple cubic lattice. The method may be readily adapted to yield Boltzmann weighted averages over clusters.