Nonuniversality of Invasion of Percolation in Two-dimensional Systems

Abstract

Employing highly efficient algorithms for simulating invasion percolation (IP) with trapping, we obtain precise estimates for the fractal dimensions of the sample-spanning cluster, the backbone, and the minimal path in a variety of two-dimensional lattices. The results indicate that these quantities are nonuniversal and vary with the coordination number Z of the lattices. In particular, while the fractal dimension Df of the sample-spanning cluster in lattices with low Z has the generally accepted value of about 1.82, it crosses over to the value of random percolation, Df≃ 1.896, if Z is large enough. Since optimal paths in strongly disordered media and minimum spanning trees on random graphs are related to IP, the implication is that these problems do not also possess universal scaling properties.