Scaling theory for the statistics of self-avoiding walks on random lattices

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Abstract
The authors study self-avoiding walks (SAW) on randomly diluted (quenched) lattices with direct configurational averaging over the moments of the SAW distribution function. A scaling function representation of RN, the average end-to-end distance of N-step walks, is studied here both for SAW on (a) the infinite percolation cluster and (b) any cluster. They have shown that, at the percolation threshold nu P= nu P(1- beta P/2 nu P), where beta P and nu P are the percolation order parameter and correlation length exponents respectively. The authors also propose a scaling function representation for the total number of N-step SAW configuration GN( approximately mu NNgamma -1) for infinite cluster averaging, which gives gamma P= gamma +d( nu P- nu ). For all cluster averaging gamma will remain unchanged.

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