Depinning of stiff directed lines in random media

TL;DR

This paper investigates the depinning transition of stiff directed lines in random media, revealing unique critical behavior and extending theoretical models to account for bending rigidity effects.

Contribution

It provides the first detailed analysis of depinning for lines governed by bending rigidity, including critical exponents and the extension of functional renormalization group methods.

Findings

Identification of critical exponents for stiff directed lines

Evidence for two distinct correlation length exponents

Comparison with previous theoretical and numerical results

Abstract

Driven elastic manifolds in random media exhibit a depinning transition to a state with non-vanishing velocity at a critical driving force. We study the depinning of stiff directed lines, which are governed by a bending rigidity rather than line tension. Their equation of motion is the (quenched) Herring-Mullins equation, which also describes surface growth governed by surface diffusion. Stiff directed lines are particularly interesting as there is a localization transition in the static problem at a finite temperature and the commonly exploited time ordering of states by means of Middleton's theorems (A. Middleton, Phys. Rev. Lett. 68, 670 (1992)) is not applicable. We employ analytical arguments and numerical simulations to determine the critical exponents and compare our findings with previous works and functional renormalization group results, which we extend to the different line elasticity. We see evidence for two distinct correlation length exponents.