Marginal Pinning of Quenched Random Polymers

An elastic string embedded in 3D space and subject to a short-range correlated random potential exhibits marginal pinning at high temperatures, with the pinning length $L_c(T)$ becoming exponentially sensitive to temperature. Using a functional renormalization group (FRG) approach we find $L_c(T)\propto \exp [(32\mathrm{/}\pi )(T\mathrm{/}{T}_{\mathrm{d}\mathrm{p}}{)}^3]$, with $T_{\mathrm{d}\mathrm{p}}$ the depinning temperature. A slow decay of disorder correlations as it appears in the problem of flux line pinning in superconductors modifies this result, $\ln L_c(T)\propto T^{3/2}$.