Diffusion trapping times and dynamic percolation in an Ising system

We address the problem of diffusion through dynamic Ising network structures using random walkers (RWs) whose net displacements are partitioned into two contributions, arising from (1) transport through neighboring "conducting" clusters and (2) self-diffusion of the site on which the RW finds itself, respectively. At finite temperatures, the conducting clusters in the network exhibit correlated dynamic behavior, making our model system different to most prior published work, which has largely been at the random percolation limit. We also present a novel heuristic scaling analysis for this system that utilizes a new scaling exponent theta(z) for representing RW trapping time as a function of "distance" from the dynamic percolation transition. Simulation results in two-dimensional networks show that when theta(z) = 2, a value found from independent physical arguments, our scaling equations appear to capture universal behavior in the system, at both the random percolation (infinite temperature) and finite temperature conditions studied. This study suggests that the model and the scaling approach given here should prove useful for studying transport in physical systems showing dynamic disorder.