Universal Scaling Functions for Numbers of Percolating Clusters on Planar Lattices.

Abstract

Using a histogram Monte Carlo method and nonuniversal metric factors of a recent Letter [Phys. Rev. Lett. 75, 193 (1995)], we find that the probability for the appearance of $n$, $n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1,2,\dots{},$ top to bottom percolating clusters on finite square, planar triangular, and honeycomb lattices falls on the same universal scaling functions, which show interesting behavior as the aspect ratio of the lattice increases. Our results suggest many interesting problems for further research.