Depinning in a Random Medium

TL;DR

This paper develops a continuum field theory for a directed polymer in a random medium with an extended defect, revealing a second-order phase transition and providing analytic critical parameters, with implications for surface growth models.

Contribution

It introduces a renormalized field theory incorporating operator algebra for pinning, addressing hyperscaling breakdown, and analytically characterizing the depinning transition.

Findings

Identifies a second-order phase transition between localized and delocalized phases.

Provides analytic expressions for critical pinning strength and scaling exponents.

Links depinning phenomena to inhomogeneous KPZ surface growth.

Abstract

We develop a renormalized continuum field theory for a directed polymer interacting with a random medium and a single extended defect. The renormalization group is based on the operator algebra of the pinning potential; it has novel features due to the breakdown of hyperscaling in a random system. There is a second-order transition between a localized and a delocalized phase of the polymer; we obtain analytic results on its critical pinning strength and scaling exponents. Our results are directly related to spatially inhomogeneous Kardar-Parisi-Zhang surface growth.