Disorder-Induced Depinning Transition

TL;DR

This paper investigates how disorder affects the pinning and depinning transition of directed polymers, revealing marginal localization in 1+1 dimensions and analyzing critical behavior in higher dimensions using renormalization group methods.

Contribution

It provides a systematic analysis of disorder-induced depinning transitions using renormalization group, mapping to noisy-Burgers' equation, and mode-coupling techniques, offering new insights into localization phenomena.

Findings

Directed polymer is marginally localized to weak columnar pins in 1+1 dimensions.

Large scale, nearly degenerate optimal paths cause weak localization.

Critical behavior of depinning transition characterized above 1+1 dimensions via epsilon-expansion.

Abstract

The competition in the pinning of a directed polymer by a columnar pin and a background of random point impurities is investigated systematically using the renormalization group method. With the aid of the mapping to the noisy-Burgers' equation and the use of the mode-coupling method, the directed polymer is shown to be marginally localized to an arbitrary weak columnar pin in 1+1 dimensions. This weak localization effect is attributed to the existence of large scale, nearly degenerate optimal paths of the randomly pinned directed polymer. The critical behavior of the depinning transition above 1+1 dimensions is obtained via an $\epsilon$-expansion.