Finite-size scaling in two-dimensional continuum percolation models

We test the universal finite-size scaling of the cluster mass order paramet er in two-dimensional (2D) isotropic and directed continuum percolation mod els below the percolation threshold by computer simulations. We found that the simulation data in the 2D continuum models obey the same scaling expres sion of mass M to sample size L as generally accepted for isotropic lattice problems, but with a positive sign of the slope in the In-in plot of M ver sus L. Another interesting aspect of the finite-size 2D models is also sugg ested by plotting the normalized mass in 2D continuum and lattice bond perc olation models versus an effective percolation parameter, independent of th e system structure (i.e., lattice or continuum) and of the possible directi ons allowed for percolation (i.e., isotropic or directed) in regions close to the percolation thresholds, Our study is the first attempt to map the sc aling behavior of the mass for both lattice and continuum model systems int o one curve.