Different types of self-avoiding walks on deterministic fractals

Y. Shussman, A. Aharony

Research output: Contribution to journalArticlepeer-review

Abstract

"Normal" and indefinitely-growing (IG) self-avoiding walks (SAWs) are exactly enumerated on several deterministic fractals (the Manderbrot-Given curve with and without dangling bonds, and the 3-simplex). On the n th fractal generation, of linear size L, the average number of steps behaves asymptotically as 〈N〉=ALDsaw+B. In contrast to SAWs on regular lattices, on these factals IGSAWs and "normal" SAWs have the same fractal dimension Dsaw. However, they have different amplitudes (A) and correction terms (B).

Original languageEnglish
Pages (from-to)545-563
Number of pages19
JournalJournal of Statistical Physics
Volume77
Issue number3-4
DOIs
StatePublished - Nov 1994

Keywords

  • Self-avoiding walks
  • fractals
  • indefinitely-growing self-avoiding walks
  • renormalization

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