Is the Alexander–Orbach Conjecture Suitable for Treating Diffusion in Correlated Percolation Clusters?

Abstract

How does a particle diffuse inside a percolation cluster? This question is of both scientific and practical importance, e.g. in drug-controlled release and vapour adsorption. Diffusion in fractal media is characterized by the fracton dimension, d s . The Alexander and Orbach conjecture indicates that d s = 4/3 for diffusion in classical percolation clusters and, after much research on the subject, it is still provides a very good approximation for d s in the case of uncorrelated percolation cluster structures. However, what happens to the value of d s when a particle is moving inside a correlated percolation cluster? In this work, this problem is studied via Monte Carlo computer simulation. Our results show that the Alexander and Orbach conjecture is not always fulfilled.