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

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

2001-02-22

arxiv.org/abs/cond-mat/0102408v1

Phys. Rev. E 61, 20104R (2001)

Physics

Condensed Matter

Disordered Systems and Neural Networks

7 pages, 1 postscript figure

Scientific paper

10.1103/PhysRevE.63.020104

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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