Universality of amplitude combinations in two-dimensional percolation

We generated/extended low concentration series for the second moment of distances between cluster points A₂ in site and bond percolation on the square lattice and used them to calculate series for the correlation length ξ. We analysed these and other series for their critical amplitudes, and compared them with results from Monte Carlo simulations of triangular site, square site, and square bond percolation. The values obtained from the different models for the amplitude combination B²ξ²₀/ Γ₂ (ξ₀, Γ₂, and B are the amplitudes of ξ, the second moment of the cluster size distribution M₂, and the strength of the infinite cluster P, respectively), are all within the range 2.23 ± 0.10, confirming universality.