A Kinetics Driven Commensurate - Incommensurate Transition

Abstract

The steady state structure of an interface in an Ising system on a square lattice placed in a 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