Universality of amplitude combinations in two-dimensional percolation

We generated/extended low concentration series for the second moment of dis tances between cluster points A(2) in site and bond percolation on the squa re lattice and used them to calculate series for the correlation length xi. We analysed these and other series for their critical amplitudes, and comp ared them with results from Monte Carlo simulations of triangular site, squ are site, and square bond percolation. The values obtained from the differe nt models for the amplitude combination B(2)xi(0)(2)/Gamma(2) (xi(0), Gamma (2), and B are the amplitudes of xi, the second moment of the cluster size distribution M-2, and the strength of the infinite cluster P, respectively) , are all within the range 2.23 +/- 0.10, confirming universality.