1 research outputs found
Multifractal behavior of linear polymers in disordered media
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 \mu_q
and enhancement exponents \gamma_q, which depend on q. Our numerical results
suggest that the relation \mu_1 = p_ c \mu between the first moment \mu_1 and
its regular lattice counterpart \mu is valid.Comment: 11 pages, 12 postscript figures, to be published in Phys. Rev.