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`Generalized des Cloizeaux' exponent for self-avoiding walks on the incipient percolation cluster

Anke Ordemann·Markus Porto·H. Eduardo Roman·Shlomo Havlin
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Abstract

We study the asymptotic shape of self-avoiding random walks (SAW) on the backbone of the incipient percolation cluster in d-dimensional lattices analytically. It is generally accepted that the configurational averaged probability distribution function for the end-to-end distance r of an N step SAW behaves as a power law for r -> 0. In this work, we determine the corresponding exponent using scaling arguments, and show that our suggested `generalized des Cloizeaux' expression for the exponent is in excellent agreement with exact enumeration results in two and three dimensions.

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Anke Ordemann, Markus Porto, H. Eduardo Roman, Shlomo Havlin. 2001-02-22. `Generalized des Cloizeaux' exponent for self-avoiding walks on the incipient percolation cluster. https://doi.org/10.1103/physreve.63.020104

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