Statistics of the two self-avoiding random walks on the three-dimensional fractal lattices

Abstract

We present results of the effects of interpenetration of two interacting self-avoiding walks that take place in a member of a three-dimensional Sierpinski Gasket (SG) fractal family. We focus our attention on finding number of point contacts between the two SAW paths, which turns out to be a set of power laws whose characteristics depend predominantly on the given interactions between SAW steps. To establish statistics of the defining model, we apply an exact Renormalization Group Method for the few members (b = 2, 3 and 4) of the SG fractal family, as well as a Monte Carlo RG method for 2 ≤ b ≤ 25. The phase diagrams have been established and relevant values of the contact critical exponents, associated with the two-path mutual contacts, are determined. © 2007 Elsevier Ltd. All rights reserved.