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 sx(τ) ∝ τφ. For masses s ≪ sx, the grown clusters are percolation clusters, being compact for p > pc. For s ≫ sx, the generated structures belong to the universality class of self-avoiding walk with a fractal dimension df = 4/3 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/sx(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.
Ordemann, A., Roman, H., Bunde, A. (1999). Cluster growth at the percolation threshold with a finite lifetime of growth sites. PHYSICA. A, 266(1-4), 92-95 [10.1016/S0378-4371(98)00580-9].
Cluster growth at the percolation threshold with a finite lifetime of growth sites
Roman H. E.;
1999
Abstract
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 sx(τ) ∝ τφ. For masses s ≪ sx, the grown clusters are percolation clusters, being compact for p > pc. For s ≫ sx, the generated structures belong to the universality class of self-avoiding walk with a fractal dimension df = 4/3 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/sx(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.
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