Exact and Monte Carlo study of the two self-avoiding random walks on the three-dimensional Sierpinski lattices

Abstract

We consider the phenomena of entanglement of the two interacting self-avoiding walks (SAW) situated in a member of the three-dimensional Sierpinski Gasket (SG) fractal family. We focus our attention to determine number of point contacts between the two SAW paths M, which turns out to be a set of power laws whose characteristics depend predominantly on the interactions between SAW steps. The phase diagrams have been established and corresponding values of the contact critical exponents φ, associated with the two-path mutual contacts, have been found. © 2007 American Institute of Physics.