Structure of self-avoiding walks on percolation clusters at criticality

H. Eduardo Roman, Anke Ordemann, Markus Porto, Armin Bunde, Shlomo Havlin

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


The structure of linear polymers modelled by self-avoiding random walks (SAWs) on the backbone of two-dimensional percolation clusters at criticality is studied. To this end, all possible SAW configurations of N steps on a single-backbone configuration are enumerated exactly, and averages over many backbone configurations are performed to extract the mean quantities of interest. We determine the critical exponents describing the structure of SAWs, in both Euclidean and topological space, and the corresponding mean distribution functions for the end-to-end distance after N steps. A relation between the exponents characterizing the asymptotic shape of these distributions and those describing the total number of SAWS of N steps on the backbone is suggested and supported by numerical results.

Original languageEnglish
Pages (from-to)1357-1371
Number of pages15
JournalPhilosophical Magazine B: Physics of Condensed Matter; Statistical Mechanics, Electronic, Optical and Magnetic Properties
Issue number5
StatePublished - May 1998


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