Critical region of long-range depinning transitions

Abstract

The depinning transition of elastic interfaces with an elastic interaction kernel decaying as 1/rd+σ is characterized by critical exponents which continuously vary with σ. These exponents are expected to be unique and universal, except in the fully coupled (−d<σ≤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 limits in terms of the vanishing of the critical region for smooth potentials, as we decrease σ from the short-range (σ≥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 nonlocal elasticity, such as contact lines of liquids and fractures.