Universality of amplitude combinations in two-dimensional percolation

Universal amplitude ratio Gamma-/Gamma+ for two-dimensional percolation

The amplitude ratio of the susceptibility (or second size moment) for two-dimensional percolation is calculated by two series methods and also by Monte Carlo simulation. The first series method is an approach based upon integrating approximations to the scaling function. The second series method directly uses low- and high-density series expansions of the susceptibility, going to unprecedented orders for both bond and site percolation on the square lattice. Putting all methods together we find a consistent value Gamma-/Gamma+ = 162.5+/-2 , a significant improvement over previous results that placed the value of this ratio variously in the range of 14 to 220.