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Kinetic growth walk on critical percolation clusters and lattice animals

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Abstract

The statistics of recently proposed kinetic growth walk (KGW) model for linear polymers (or growing self avoiding walk (GSAW)) on two dimensional critical percolation clusters and lattice animals are studied using real-space renormalization group method. The correlation length exponents ν's are found to be ν KGW Pc = 0.68 and ν KGW LA respectively for the critical percolation clusters and lattice animals. Close agreements are found between these results and a generalized Flory formula for linear polymers at theta point ν KGW F = 2/\(\bar d\)+1),, where\(\bar d\) is the fractal dimension of the fractal objectF.

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Lam, P.M., Zhang, Z.Q. Kinetic growth walk on critical percolation clusters and lattice animals. Z. Physik B - Condensed Matter 57, 65–69 (1984). https://doi.org/10.1007/BF01679927

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Keywords

  • Polymer
  • Spectroscopy
  • Neural Network
  • State Physics
  • Complex System