Diffusion and polymers in fractal, disordered environments

Abstract

We numerically investigate random walks (RWs) and self-avoiding random walks (SAWs) on critical percolation clusters, basic models for diffusion and flexible polymers in disordered media. While this can be easily done for RWs using a simple enumeration method, it is difficult for long SAWs due to the long-range correlations. We employed a sophisticated algorithm that makes use of the self-similar structure of the critical clusters and allows exact enumeration of several thousand SAW steps. We also investigate a kinetic version of the SAW, the so-called kinetic growth (self-avoiding) walk (KGW), as well static averaging over all RW conformations, which describes the so-called ideal chain. For the KGW, we use a chain-growth Monte Carlo method which is inspired by the pruned-enriched Rosenbluth method. The four walk types are found to be affected in different ways by the fractal, disordered structure of the critical clusters. The simulations were carried out in two and three dimensions.