CORRECTION-TO-SCALING OF RANDOM WALKS IN DISORDERED MEDIA

Abstract

We study the correction to scaling of the rms displacements of random walks in disordered media consisted of connected networks of the lattice percolation in two, three, and four dimensions. The two types of ensemble averages, i.e. an infinite-network average of random walks starting from an infinite network and an all-cluster average starting from any occupied site, are investigated using both the myoptic ants and the blind ants models. We find that the rms displacements exhibit strong nonanalytic corrections in all dimensions. The correction exponent δ defined by the rms displacement of t-step random walks via Rt=At1/d w (1+Bt-δ+Ct-1+⋯) was found as δ≃0.39, 0.27, and 0.27 for, respectively, two, three, and four dimensions for an infinite-network average, and δ≃0.37, 0.28, and 0.24 for an all-cluster average.