Universal behavior of the amplitude ratio of percolation susceptibilities for off-lattice percolation models

We study the amplitude ratio of percolation susceptibilities, $R=\frac{C_{-}}{C_{+}}$ ($C_{-}$ and $C_{+}$ being the amplitudes below and above the percolation threshold), which is supposed to be universal but has been found to be different for certain continuum models from that of the ordinary lattice percolation. We specifically consider two off-lattice percolation models, the continuum percolation of the penetrable-concentric-shell model and the randomly bonded percolation model, for both of which $R$ was found to be different from the lattice value while various critical exponents remain the same. By numerical investigation we find that $R$ depends on the size of the system for both models; after a finite-size effect is carefully taken into account, $R$ is consistent with the lattice value, indicating a strong universality between lattice and off-lattice percolation models. We also discuss some subtleties of the finite-size scaling analyses.