Universal macroscopic background formation in surface super-roughening

TL;DR

This paper reveals that super-rough surface growth models universally develop a macroscopic polynomial background that influences local surface scaling, but can be separated to recover standard Family-Vicsek scaling.

Contribution

It introduces the concept of a universal macroscopic background in super-rough models and demonstrates its impact on surface scaling behavior.

Findings

Macroscopic background forms spontaneously in super-rough models

Subtracting the background restores Family-Vicsek scaling

Background shape is a finite-order polynomial related to the roughness exponent

Abstract

We study a class of super-rough growth models whose structure factor satisfies the Family-Vicsek scaling. We demonstrate that a macroscopic background spontaneously develops in the local surface profile, which dominates the scaling of the local surface width and the height-difference. The shape of the macroscopic background takes a form of a finite-order polynomial whose order is decided from the value of the global roughness exponent. Once the macroscopic background is subtracted, the width of the resulting local surface profile satisfies the Family-Vicsek scaling. We show that this feature is universal to all super-rough growth models, and we also discuss the difference between the macroscopic background formation and the pattern formation in other models.