Depinning of elastic manifolds

TL;DR

This paper computes the roughness exponents of elastic manifolds at the depinning transition using a Hamiltonian-based numerical method, revealing stability issues and connections to the quenched KPZ class.

Contribution

It introduces a Hamiltonian-based numerical approach to determine critical manifolds and exponents for elastic manifolds at depinning, including anharmonic effects.

Findings

Roughness exponents between one-loop and two-loop RG results.

Harmonic model is unstable to elastic potential variations.

Anharmonic corrections yield exponents of the quenched KPZ class.

Abstract

We compute roughness exponents of elastic d-dimensional manifolds in (d+1)-dimensional embedding spaces at the depinning transition for d=1,...,4. Our numerical method is rigorously based on a Hamiltonian formulation; it allows to determine the critical manifold in finite samples for an arbitrary convex elastic energy. For a harmonic elastic energy, we find values of the roughness exponent between the one-loop and the two-loop functional renormalization group result, in good agreement with earlier cellular automata simulations. We find that the harmonic model is unstable with respect both to slight stiffening and to weakening of the elastic potential. Anharmonic corrections to the elastic energy allow us to obtain the critical exponents of the quenched KPZ class.