Multifractal behavior of linear polymers in disordered media

Abstract

The scaling behavior of linear polymers in disordered media modelled by self-avoiding random walks (SAWs) on the backbone of two- and three-dimensional percolation clusters at their critical concentrations p_c is studied. All possible SAW configurations of N steps on a single backbone configuration are enumerated exactly. We find that the moments of order q of the total number of SAWs obtained by averaging over many backbone configurations display multifractal behavior, i.e. different moments are dominated by different subsets of the backbone. This leads to generalized coordination numbers μ_q and enhancement exponents γ_q, which depend on q. Our numerical results suggest that the relation μ_1 = p_ c μbetween the first moment μ_1 and its regular lattice counterpart μis valid.