How to measure Functional RG fixed-point functions for dynamics and at depinning

TL;DR

This paper demonstrates how to directly measure the renormalized force correlator in functional RG theory through numerical and experimental methods, revealing new insights into elastic manifold dynamics and depinning phenomena.

Contribution

It introduces a practical approach to measure the FRG function Delta(u) in experiments and simulations, extending its application from equilibrium to depinning regimes.

Findings

Delta(u) can be measured directly in experiments and numerics.

The relation between Delta(u) and physical observables is confirmed for equilibrium.

In the depinning regime, Delta(u) shows a cusp and differs from static cases.

Abstract

We show how the renormalized force correlator Delta(u), the function computed in the functional RG (FRG) field theory, can be measured directly in numerics and experiments on the dynamics of elastic manifolds in presence of pinning disorder. For equilibrium dynamics we recover the relation obtained recently in the statics between Delta(u) and a physical observable. Its extension to depinning reveals interesting relations to stick-slip models of avalanches used in dry friction and earthquake dynamics. The particle limit (d=0) is solved for illustration: Delta(u) exhibits a cusp and differs from the statics. We propose that the FRG functions be measured in wetting and magnetic interfaces experiments.