Kinetic growth walks and trails on oriented square lattices: Hull percolation and percolation hulls

Abstract

We have studied kinetic growth walks on the Manhattan lattice and kinetic growth trails onthe L lattice. We find that the directional properties of these lattices prevent the kinetic growthwalks from being trapped (except at the origin). As a consequence, KGWS are found to be in the SKWuniversality class for these lattices. Extensive numerical calculations support this fact. Moreover it has been shown that the recently introduced hull percolation is equivalent to the kinetic growth walks on the Manhattan lattice, and the bond percolation hull on the square lattice at the percolation threshold is equivalent to the kinetic growth trails on the L lattice. Our numerical estimates agree nicely wi..