Self-avoiding walks on random fractal environments

Yossi Shussman*, Amnon Aharony

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Self-avoiding random walks (SAWs) are studied on several hierarchical lattices in a randomly disordered environment. An analytical method to determine whether their fractal dimension Dsaw is affected by disorder is introduced. Using this method, it is found that for some lattices, Dsaw is unaffected by weak disorder; while for others Dsaw changes even for infinitestimal disorder. A weak disorder exponent λ is defined and calculated analytically [λ measures the dependence of the variance in the partition function (or in the effective fugacity per step)v∼Lλ on the end-to-end distance of the SAW, L]. For lattices which are stable against weak disorder (λ<0) a phase transition exists at a critical value v=v* which separates weak- and strong-disorder phases. The geometrical properties which contribute to the value of λ are discussed.

Original languageEnglish
Pages (from-to)147-167
Number of pages21
JournalJournal of Statistical Physics
Issue number1-2
StatePublished - Jul 1995


  • Self-avoiding walks
  • disordered environment
  • fractals
  • hierarchical lattices
  • renormalization


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