A continuum percolation model in an anisotropic medium: dimensional crossover?

Abstract

We propose a two-dimensional continuum percolation model in an anisotropic medium, which consists of parallel chains of sites coupled to each other weakly via rare “impurities”. By checking simultaneously two percolations, parallel and perpendicular to the chain direction, we show that while there is a quasi-one-dimensional to two-dimensional crossover in the percolation radius of finite systems as the “impurity” density s increases, in the limit of infinite systems two percolations are equivalent in the sense that their main characters are, respectively, coincident, regardless of s. The proposed model is assumed to be used for describing hopping conduction networks in the compounds such as conjugated polymers or porous silicon.