Universal Scaling Functions in Critical Phenomena

A histogram Monte Carlo method is used to evaluate the existence probability Eₚ and the percolation probability P of bond and site percolation on finite square, plane triangular, and honeycomb lattices. We find that, by choosing a very small number of nonuniversal metric factors, all scaled data of Eₚ and P may fall on the same universal scaling functions. We also find that free and periodic boundary conditions share the same nonuniversal metric factors. This study may be extended to many critical systems.