Marginal Pinning of Quenched Random Polymers

TL;DR

This paper investigates the temperature-dependent pinning behavior of a 3D elastic string in a random potential, revealing an exponential sensitivity of the pinning length to temperature through a functional renormalization group analysis.

Contribution

It introduces a FRG-based analysis of marginal pinning in quenched polymers, deriving explicit temperature dependence of the pinning length and considering disorder correlation effects.

Findings

Pinning length $L_c(T)$ scales exponentially with temperature.

Disorder correlation decay modifies $L_c(T)$ to a logarithmic dependence.

Derived explicit formulas for $L_c(T)$ in different disorder regimes.

Abstract

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 $L_c(T) \propto \exp[(32/\pi)(T/T_{\rm dp})^3]$, with $T_{\rm dp}$ the depinning temperature. A slow decay of disorder correlations as it appears in the problem of flux line pinning in superconductors modifies this result, $\ln L_c(T)\propto T^{3/2}$.