UNIVERSAL SCALING FUNCTIONS FOR SITE AND BOND PERCOLATIONS ON PLANAR LATTICES

Universality and scaling are two important concepts in the theory of c ritical phenomena. It is generally believed that site and bond percola tions on lattices of the same dimensions have the same set of critical exponents, but they have different scaling functions. In this paper, we briefly review our recent Monte Carlo results about universal scali ng functions for site and bond percolation on planar lattices. We find that, by choosing an aspect ratio for each lattice and a very small n umber of non-universal metric factors, all scaled data of the existenc e probability E(p) and the percolation probability P for site and bond percolations on square, plane triangular, and honeycomb lattices may fall on the same universal scaling functions. We also find that free a nd periodic boundary conditions share the same non-universal metric fa ctors, When the aspect ratio of each lattice is reduced by the same fa ctor, the non-universal metric factors remain the same. The implicatio ns of such results are discussed.