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 τ and are available with a probability p. For finite τ, the clusters are characterized by a crossover mass s×(τ)∝τφ. For masses s⪡s×, the grown clusters are percolation clusters, being compact for p>pc. For s⪢s×, the generated structures belong to the universality class of self-avoiding walk with a fractal dimension df=43 for p=1 and df≅1.28 for p=pc in d=2. We find that the number of clusters of mass s scales as N(s)=N(0)exp[−s/s×(τ)], indicating that in contrary to earlier assumptions, the asymptotic behavior of the structure is determined by rare events which get more unlikely as τ increases.