Discontinuous Interface Depinning from a Rough Wall

TL;DR

This paper investigates how the roughness of a substrate affects the depinning transition of an interface, revealing that increased roughness can cause a transition to become discontinuous and potentially first-order.

Contribution

It demonstrates that substrate roughness influences the depinning transition, leading to discontinuous behavior and identifying a tricritical point, with implications for critical wetting on rough surfaces.

Findings

Depinning is continuous for substrate roughness exponent $\,<1/2$.

For $\, extgreater 1/2$, depinning becomes discontinuous.

In 3D, depinning is first-order for any substrate roughness $\,>0$.

Abstract

Depinning of an interface from a random self--affine substrate with roughness exponent $\zeta_S$ is studied in systems with short--range interactions. In 2$D$ transfer matrix results show that for $\zeta_S<1/2$ depinning falls in the universality class of the flat case. When $\zeta_S$ exceeds the roughness ($\zeta_0=1/2$) of the interface in the bulk, geometrical disorder becomes relevant and, moreover, depinning becomes \underline{discontinuous}. The same unexpected scenario, and a precise location of the associated tricritical point, are obtained for a simplified hierarchical model. It is inferred that, in 3$D$, with $\zeta_0=0$, depinning turns first--order already for $\zeta_S>0$. Thus critical wetting may be impossible to observe on rough substrates.