Growing smooth interfaces with inhomogeneous, moving external fields: dynamical transitions, devil's staircases and self-assembled ripples

TL;DR

This paper investigates how an interface in a 2D Ising model responds to a moving, inhomogeneous external field, revealing complex locking phenomena, ripples, and a transition to KPZ behavior at high velocities.

Contribution

It introduces a detailed analysis of interface behavior under inhomogeneous, moving fields, including devil's staircase locking structures and a transition to KPZ universality.

Findings

Lock-in structures form at low velocities with incommensurate ripples.

Lock-in structures disappear as velocity increases.

At high velocities, the interface exhibits KPZ scaling behavior.

Abstract

We study the steady state structure and dynamics of an interface in a pure Ising system on a square lattice placed in an inhomogeneous external field. The field has a profile with a fixed shape designed to stabilize a flat interface, and is translated with velocity v_e. For small v_e, the interface is stuck to the profile, is macroscopically smooth, and is rippled with a periodicity in general incommensurate with the lattice parameter. For arbitrary orientations of the profile, the local slope of the interface locks in to one of infinitely many rational values (devil's staircase) which most closely approximates the profile. These ``lock-in'' structures and ripples dissappear as v_e increases. For still larger v_e the profile detaches from the interface which is now characterized by standard Kardar-Parisi-Zhang (KPZ) exponents.