# Elastic interfaces on disordered substrates: From mean-field depinning to yielding

## TL;DR

This paper investigates a model of elastic interfaces on disordered substrates, revealing how critical exponents vary from mean-field depinning to finite-dimensional yielding, and highlighting the influence of microscopic pinning potentials.

## Contribution

It introduces a generalized elastic model that interpolates between mean-field depinning and finite-dimensional yielding, showing smooth variation of critical exponents and dependence on microscopic details.

## Key findings

- Critical exponents vary smoothly with elasticity modifications.
- Herschel-Buckley exponent depends on the microscopic pinning potential.
- Yielding in finite dimensions appears as a mean-field transition.

## Abstract

We consider a model of an elastic manifold driven on a disordered energy landscape, with generalized long range elasticity. Varying the form of the elastic kernel by progressively allowing for the existence of zero-modes, the model interpolates smoothly between mean field depinning and finite dimensional yielding. We find that the critical exponents of the model change smoothly in this process. Also, we show that in all cases the Herschel-Buckley exponent of the flowcurve depends on the analytical form of the microscopic pinning potential. This is a compelling indication that within the present elastoplastic description yielding in finite dimension $d\geq 2$ is a mean-field transition.