Directed self-avoiding walks on certain directed random fractals

Abstract

Using the recently proposed real space renormalisation group method for directed systems, the authors study the critical behaviour of directed self-avoiding walks (DSAW) on both directed lattice animals (DLA) and directed percolation clusters at threshold pc (DPC) in two dimensions. The values for the exponent nu perpendicular to are found to be nu perpendicular to DSAWDLA approximately=0.590 and nu perpendicular to DSAWDPC approximately=0.528, both of which are higher than the mean-field value 0.5. It is also shown rigorously that nu /sub /// remains unchanged; i.e. nu /sub //DSAW/DLA= nu /sub //DSAW/DPC=1.