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 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 obtain a Monte Carlo estimate of 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.
 Publication:

Physical Review E
 Pub Date:
 July 2000
 DOI:
 10.1103/PhysRevE.62.1397
 arXiv:
 arXiv:physics/9911023
 Bibcode:
 2000PhRvE..62.1397C
 Keywords:

 02.70.Lq;
 05.50.+q;
 Lattice theory and statistics;
 Physics  Computational Physics
 EPrint:
 18 Pages, 3 postscript figures: Submitted to Physical Review E