Growing kinetics for self-avoiding walks on diluted lattices.

Abstract

Two growing kinetics of self-avoiding walks on dilute lattices are considered for discussion of the crossover scaling behavior of self-avoiding walks near percolation threshold. The crossover properties for each kinetics are exactly calculated on a diluted linear chain and on a Cayley tree. We also consider crossover properties for each kinetics on general lattices. From the results the recent controversies of self-avoiding walks near the threshold are analyzed.