Profile driven interfaces in 1 + 1 dimensions : periodic steady states, dynamical melting and detachment

Abstract

We study the steady state structure and dynamics of a 2-d Ising interface placed in an inhomogeneous external field with a sigmoidal profile which moves with velocity $v_{e}$. In the strong coupling limit the problem maps onto an assymmetric exclusion process involving motion of particles in 1-d with position dependent right and left jump probabilities. For small $v_{e}$, the interface is stuck to the field profile. As $v_{e}$ increases the profile detaches from the interface. At the transition point(and beyond), the interfacial structure and dynamics is characterized by KPZ exponents. For small $v_{e}$, on the other hand, the interface is macroscopically smooth with a vanishing roughness exponent $α$. The interfacial structure is periodic with a periodicity which depends on the orientation of the interface. For a fixed orientation this periodic structure ``melts'' as $v_e$ is increased. We determine the dynamical ``phase - diagram'' of this system in the $v_e$ - orientation plane.