Percolation of aligned rigid rods on two-dimensional square lattices

Abstract

The percolation behavior of aligned rigid rods of length k (kmers) on two-dimensional square lattices has been studied by numerical simulations and finite-size scaling analysis. The kmers, containing k identical units (each one occupying a lattice site), were irreversibly deposited along one of the directions of the lattice. The process was monitored by following the probability RL,k(p) that a lattice composed of L×L sites percolates at a concentration p of sites occupied by particles of size k. The results, obtained for k ranging from 1 to 14, show that (i) the percolation threshold exhibits a decreasing function when it is plotted as a function of the kmer size; (ii) for any value of k (k>1), the percolation threshold is higher for aligned rods than for rods isotropically deposited; (iii) the phase transition occurring in the system belongs to the standard random percolation universality class regardless of the value of k considered; and (iv) in the case of aligned kmers, the intersection points of the curves of RL,k(p) for different system sizes exhibit nonuniversal critical behavior, varying continuously with changes in the kmer size. This behavior is completely different to that observed for the isotropic case, where the crossing point of the curves of RL,k(p) do not modify their numerical value as k is increased.