Scaling behavior of linear polymers in disordered media

Details Scaling behavior of linear polymers in disordered media Scaling behavior of linear polymers in disordered media

2006-09-04

arxiv.org/abs/cond-mat/0609053v2

Phys. Rev. E 75, 020801(R) (2007)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 3 figures

Scientific paper

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 $\nu^{(\alpha)}$.

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