Depinning transition at the upper critical dimension

TL;DR

This paper investigates the depinning transition of a driven elastic interface at the upper critical dimension, revealing logarithmic corrections to correlation functions and force-velocity characteristics using the functional renormalization group.

Contribution

It provides a detailed analysis of the depinning transition at the upper critical dimension, highlighting new logarithmic behaviors in correlation functions and force-velocity relations.

Findings

Displacement correlation function behaves as ln(x)^{2/3} at large distances.

Force-velocity relation includes a |ln(f)|^{2/9} correction.

Correlation length scales as f^{-1/2}|ln(f)|^{1/6}.

Abstract

We study the effect of quenched random field disorder on a driven elastic interface close to the depinning transition at the upper critical dimension d_{c}=4 using the functional renormalization group. We have found that the displacement correlation function behaves with distance x as ln(x)^{2/3} for large x. Slightly above the depinning transition the force-velocity characteristics is described by the equation v ~ f |ln(f)|^{2/9}, while the correlation length behaves as L_{v} ~ f^{-1/2}|ln(f)|^{1/6}, where f=F/F_{c}-1 is the reduced driving force.