Different self-avoiding walks on percolation clusters: A small-cell real-space renormalization-group study

J. P. Hovi*, Amnon Aharony

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We calculate the average number of steps N for edge-to-edge, "normal," and indefinitely growing self-avoiding walks (SAWs) on two-dimensional critical percolation clusters, using the real-space renormalization-group approach, with small "H" cells. Our results are of the form N = ALDSAW + B, where L is the end-to-end distance. Similarly to several deterministic fractals, the fractal dimensions DSAW for these three different kinds of SAWs are found to be equal, and the differences between them appear in the amplitudes A and in the correction terms B. This behavior is attributed to the hierarchical nature of the critical percolation cluster.

Original languageEnglish
Pages (from-to)1163-1178
Number of pages16
JournalJournal of Statistical Physics
Volume86
Issue number5-6
DOIs
StatePublished - Mar 1997

Keywords

  • Corrections to scaling
  • Fractals
  • Indefinitely growing self-avoiding walks
  • Percolation clusters
  • Real-space renormalization group
  • Self-avoiding walks
  • Universality

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