On the critical region of long-range depinning transitions

TL;DR

This paper investigates how the critical behavior of long-range elastic interface depinning transitions varies with interaction range and potential smoothness, revealing a vanishing critical region in certain limits affecting universality class identification.

Contribution

It provides a detailed comparison of depinning transitions for cuspy and smooth potentials, explaining the peculiar limit behavior as the interaction becomes fully coupled.

Findings

Critical exponents vary with interaction range parameter σ.

The critical region vanishes for smooth potentials as σ approaches the fully coupled limit.

Results impact experimental determination of depinning universality classes.

Abstract

The depinning transition of elastic interfaces with an elastic interaction kernel decaying as $1/r^{d+\sigma}$ is characterized by critical exponents which continuously vary with $\sigma$. These exponents are expected to be unique and universal, except in the fully coupled ($-d<\sigma\le 0$) limit, where they depend on the "smooth" or "cuspy" nature of the microscopic pinning potential. By accurately comparing the depinning transition for cuspy and smooth potentials in a specially devised depinning model, we explain such peculiar limit in terms of the vanishing of the critical region for smooth potentials, as we decrease $\sigma$ from the short-range ($\sigma \geq 2$) to the fully coupled case. Our results have practical implications for the determination of critical depinning exponents and identification of depinning universality classes in concrete experimental depinning systems with non-local elasticity, such as contact lines of liquids and fractures.