Pores and Hausdorff dimension in fractal site-percolation systems

Site-percolation systems have been generated to simulate fractal structures. In d = 2, after removal of all finite clusters, the voids between the percolating clusters are considered to represent pores of various areas. We show that the pore size can be expressed in terms of the Hausdorff dimension D of the percolating clusters. The scaling of the pore size distribution is shown to lead to an excellent determination of D, even when the fractal persistence length ξ is rather short. This determination of D is compared those obtained by box counting, by finite size scaling, or via the pair correlation function g(r). The crossover to the homogeneous regime for systems of finite Ornstein-Zernike ξ is sharp and occurs at a pore size of order 4ξ2. Granularity effects at large q are more important for q-space methods than in real space. Comparing systems of different sizes clearly separates the three regimes where granularity, scaling, or homogeneity dominate.