Folklore has, that the universal scaling properties of linear polymers in disordered media are well described by the statistics of self-avoiding walks Folklore has, that the universal scaling properties of linear polymers in disordered media are well described by the statistics of self-avoiding walks (SAWs) on percolation clusters and their critical exponent $\nu_{ \text{ SAW}}$, with SAW implicitly referring to \emph{ average} SAW. Hitherto, static averaging has been commonly used, e.g. in numerical simulations, to determine what the \emph{ average} SAW is. We assert that only kinetic, rather than static, averaging can lead to asymptotic scaling behavior and corroborate our assertion by heuristic arguments and a renormalizable field theory. Moreover, we calculate to two-loop order $\nu_{ \text{ SAW}}$, the exponent $\nu _{ \text{ max}}$ for the longest SAW, and a new family of multifractal exponents $\nu^{ (\alpha)}$.
Categories: cond-mat.stat-mech cond-mat.dis-nn