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Corrections to cluster-radius scaling for branched polymers and percolation

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Zeitschrift für Physik B Condensed Matter

Abstract

We report analyses of series enumerations for the mean radius of gyration for isotropic and directed lattice animals and for percolation clusters, in two and three dimensions. We allow for the leading correction to the scaling behaviour and obtain estimates of the leading correction-to-scaling exponent ϑ. We find ν-0.640±0.004 and ϑ=0.87±0.07 for isotropic animals in 2d, and ϑ=0.64±0.06 in 3d. For directed lattice animals we argue that the leading correction hasθ=ν ⊥ orθ=ν ⊥; we also estimateν ∥=0.82±0.01 and 0.69 ±0.01 ind=2, 3 respectively. For percolation clusters at and abovep c, we find ϑ(p c) =0.58±0.06 and ϑ(p>p c)=0.84±0.09 in 2d, and ϑ(p c)=0.42±0.11 and ϑ(p>p c)=0.41 ±0.09 in 3d.

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Author notes

  1. Alla Margolina

    Present address: Department of Chemical Engineering, Princeton University, 08544, Princeton, NJ, USA

Authors and Affiliations

  1. Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts, USA

    Alla Margolina

  2. Department of Physics, Emory University, 30322, Atlanta, Georgia, USA

    Fereydoon Family

  3. Baker Laboratory, Cornell University, 14853, Ithaca, New York, USA

    Vladimir Privman

Authors
  1. Alla Margolina
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  2. Fereydoon Family
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  3. Vladimir Privman
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Margolina, A., Family, F. & Privman, V. Corrections to cluster-radius scaling for branched polymers and percolation. Z. Physik B - Condensed Matter 54, 321–324 (1984). https://doi.org/10.1007/BF01485829

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  • DOI: https://doi.org/10.1007/BF01485829

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