ON THE UNIVERSALITY OF CROSSING PROBABILITIES IN 2-DIMENSIONAL PERCOLATION

Six percolation models in two dimensions are studied: percolation by sites and by bonds on square. hexagonal, and triangular lattices. Rectangles of width a and height b are superimposed on the lattices and four functions, representing the probabilities of certain crossings from one interval to another on the sides. are measured numerically as functions of the ratio a/b. In the limits set by the sample size and by the conventions and on the range of the ratio a/b measured, the four functions coincide for the six models. We conclude that the values of the four functions can be used as coordinates of the renormalization-group fixed point.