Journal of Statistical Physics, Vol. 66, Nos. 1/2, 1992 Counting Lattice Animals: A Parallel Attack Stephan Mertens 1 and Markus E. Lautenbacher 2 Received July 1.5, 1991 A parallel algorithm for the enumeration of isolated connected clusters on a regular lattice is presented. The algorithm has been implemented on 17 RISC- based workstations to calculate the perimeter polynomials for the plane triangular lattice up to clustersize s = 21. New data for perimeter polynomials Ds up to D21, total number of clusters gs up to g22, and coefficients b~ in the low-density series expansion of the mean cluster size up to b21 are given. KEY WORDS: Cluster enumeration; lattice statistics; perimeter polynomials; parallel algorithms. 1. INTRODUCTION Power series expansions in lattice statistics require the enumeration of finite connected clusters ("lattice animals" or "polyminoes"). The classical site percolation problem (*) considered here is a standard example. If p denotes the probability that a lattice site is occupied, the mean number (per lattice site) of connected clusters of occupied sites with size s is given by ns(p) = ~ gstpS(1- p)' =: p SD~.(q) (1) t with q = 1 -p. In the above equation gst denotes the number of possible clusters with size s and perimeter t and D,(q) is usually termed the perimeter polynomial. The perimeter polynomials comprise a considerable amount of information about the percolation problem. Ds(1 ) = :gs gives the total number of s-clusters per lattice site, for example, and the low-density series expansion of the mean cluster size S(p)= p-1 ~sSZns can easily be calculated from the coefficients g~,. Universit~it G6ttingen, lnstitut fiir Theoretische Physik, D-3400 G6ttingen, Germany. 2 Technische Universit~it Mfinchen, Physik Department T30, D-8046 Garching, Germany. 669 0022-4715/92/0100-0669506.50/0 1992 Plenum Publishing Corporation