A Kinetics Driven Commensurate - Incommensurate Transition

TL;DR

This paper investigates how an interface in an Ising system transitions from a flat, rippled state to a detached, coarsening state as the velocity of a non-uniform external field increases, revealing a kinetics-driven commensurate-incommensurate transition.

Contribution

It introduces a detailed phase diagram and multifractal analysis of the interface structures under a moving non-uniform field, combining numerical and analytical methods.

Findings

At low velocities, the interface is locked in commensurate or incommensurate states with a devil's staircase structure.

Increasing velocity causes a transition where the interface detaches and exhibits Kardar-Parisi-Zhang coarsening behavior.

Numerical results include the phase diagram and multifractal spectrum of the interface structures.

Abstract

The steady state structure of an interface in an Ising system on a square lattice placed in a {\em non-uniform} external field, shows a commensurate -incommensurate transition driven by the velocity of the interface. The non-uniform field has a profile with a fixed shape which is designed to stabilize a flat interface, and is translated with velocity $v_{e}$. For small velocities the interface is stuck to the profile and is rippled with a periodicity which may be either commensurate or incommensurate with the lattice parameter of the square lattice. For a general orientation of the profile, the local slope of the interface locks in to one of infinitely many rational directions producing a devil's staircase structure. These ``lock-in'' or commensurate structures dissappear as $v_e$ increases through a kinetics driven commensurate - incommensurate transition. For large $v_e$ the interface becomes detached from the field profile and coarsens with Kardar-Parisi-Zang exponents. The complete phase-diagram and the multifractal spectrum corresponding to these structures have been obtained numerically together with several analytic results concerning the dynamics of the rippled phases. Our work has technological implications in crystal growth and the production of surfaces with various desired surface morphologies.