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) proportiona l to tau(phi). For masses s much less than s(x), the grown clusters are per colation clusters, being compact for p > p(c). For s much greater than s(x) , the generated structures belong to the universality class of self-avoidin g 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 s cales as N(s) = N(0) exp[ - s/s(x)(tau)], indicating that in contrary to ea rlier assumptions, the asymptotic behavior of the structure is determined b y rare events which get more unlikely as tau increases. (C) 1999 Published by Elsevier Science B.V. All rights reserved.