Aspect-ratio dependence of percolation probability in a rectangular system

Abstract

I investigate site percolation on a rectangular system (aspect ratio a) of a square lattice for a given occupation probability p (not restricted to p(c)) using computer simulations. The dependence of the percolation probability R on a is shown and analyzed on the basis of a modified finite-size scaling function. A method for evaluating R without statistical simulations is proposed for given conditions (longitudinal dimension L, a, and p) of the system.