Monte Carlo renormalization group study of crosslinked polymer chains on fractals

Abstract

We study the problem of two crosslinked polymer chains in a good solvent, modelled by two mutually crossing self-avoiding walks situated on fractals that belong to the Sierpinski gasket (SG) family (whose members are labelled by an integer b, ). By applying the Monte Carlo renormalization group (MCRG) method, we calculate the critical exponent y associated with the number of crossings of the two self-avoiding-walk paths, for a sequence of SG fractals with . For the problem under study, we find that our MCRG approach provides results that are virtually rigorous, that is, results with exceptionally small deviations (at most 0.07%) from the available exact renormalization group results. We discuss our set of MCRG data for y as a function of the fractal parameter b, and compare its behaviour with the finite-size scaling predictions.