Lacunarity of Classical Site Percolation Spanning Clusters Built on Correlated Square Lattices

Abstract

Classical site percolation is studied on square pore networks generated through the dual site–bond model (DSBM). This model allows different strengths of correlations among the lattice elements in such a way that patches of sites and bonds with similar sizes are structured as correlations are setup. The typical size of these patches depends on the strength of correlations. The aim of this paper is to find whether the global patchy structure is responsible for the patterns found in classical percolation structures. To this end, we measure different static quantities of the correlated networks, such as correlation length, and fractal quantities of the spanning clusters. We observe a significant gap from the reported behavior. For instance, our results indicate that the fractal dimension of the spanning cluster is nonuniversal and changes with the network correlation. The DSBM is good to produce classical percolation clusters with different fractal dimension and different lacunarity behavior. Comparison with other authors’ recent findings is presented.