UNIVERSAL SCALING FUNCTIONS FOR PERCOLATION ON PLANAR LATTICES(Session I : Cross-Disciplinary Physics, The 1st Tohwa University International Meeting on Statistical Physics Theories, Experiments and Computer Simulations)

Abstract

In this paper, we briefly review our recent results in the calculation of universal scaling functions for site and bond percolation on finite square, plane triangular, and honeycomb lattices. We find that, by choosing an aspect ratio for each lattice and a very small number of nonuniversal metric factors, all scaled data of the existance probability E_p and the percolation probability P fall on the same universal scaling functions. We also find that free and periodic boundary conditions share the same nonuniversal metric factors. When the aspect ratio of each lattice is reduced by the same factor, the nonouniversal metric factors remain the same. The probabilities for the appearance of n, n=1, 2, 3, ..., percolating clusters for bond and site percolations on various planar lattices also have universal scaling functions. The implications of such results on numerical and experimental studies of critical phenomena are discussed.