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

Author

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  • Ordemann, Anke
  • Roman, H.Eduardo
  • Bunde, Armin

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 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.

Suggested Citation

  • Ordemann, Anke & Roman, H.Eduardo & Bunde, Armin, 1999. "Cluster growth at the percolation threshold with a finite lifetime of growth sites," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 266(1), pages 92-95.
  • Handle: RePEc:eee:phsmap:v:266:y:1999:i:1:p:92-95
    DOI: 10.1016/S0378-4371(98)00580-9
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