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

Abstract

The authors have studied kinetic growth walks on the Manhattan lattice and kinetic growth trails on the L lattice. They find that the directional properties of these lattices prevent the kinetic growth walks from being trapped (except at the origin). As a consequence, KGWs are found to be in the SKW universality 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. Their numerical estimates agree nicely with the original estimates, and thus support the equivalence.