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Radius, perimeter, and density profile for percolation clusters and lattice animals

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Zeitschrift für Physik B Condensed Matter

Abstract

Monte Carlo simulation and “series expansion” shows the radius of gyration of large clusters withs sites each to vary ass ρ withρ≃0.56 in two andρ≃0.47 in three dimensions at the percolation threshold, and withρ(d=2)≃0.65 andρ(d=3)≃0.53 for random lattice animals (zero concentration). Clusters up tos=100 were used. The perimeter of random animals approaches 2.8s for larges on the simple cubic lattice. Monte Carlo simulation of the Eden process (“growing animals”) up tos=5,000 indicates a systematic variation of about ±0.05 for the effective exponentρ=ρ(s) and thus suggests that the true asymptotic exponents may be compatible with the predictions of “hyper”-scaling.

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Authors and Affiliations

  1. Institut für Theoretische Physik, Universität zu Köln, Zülpicher Straße 77, D-5000, Köln 41, Germany

    H. P. Peters, D. Stauffer, H. P. Hölters & K. Loewenich

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  1. H. P. Peters
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  2. D. Stauffer
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  3. H. P. Hölters
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  4. K. Loewenich
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Peters, H.P., Stauffer, D., Hölters, H.P. et al. Radius, perimeter, and density profile for percolation clusters and lattice animals. Z Physik B 34, 399–408 (1979). https://doi.org/10.1007/BF01325205

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  • DOI: https://doi.org/10.1007/BF01325205

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