Cluster growth at the percolation threshold with a finite lifetime of growth sites

We revisit, by means of Monte Carlo simulations and scaling arguments, the growth model of Bunde et al. (J. Stat. Phys. 47 (1987) 1)where growth sites have a lifetime tau and are available with a probability p. For finite tau, the clusters are characterized by a crossover mass s (x)(tau) proportional to tau(phi). For masses s much less than s(x), the grown clusters are percolation clusters, being compact for p > p(c). For s much greater than s(x), the generated structures belong to the universality class of self-avoiding walk with a fractal dimension d(f) = 4/3 for p = 1 and d(f) congruent to 1.28 for p = p(c) in d = 2. We find that the number of clusters of mass s scales as N(s) = N(0) exp[ - s/s(x)(tau)], indicating that in contrary to earlier assumptions, the asymptotic behavior of the structure is determined by rare events which get more unlikely as tau increases. (C) 1999 Published by Elsevier Science B.V. All rights reserved.