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

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 ve. In the strong coupling limit, the problem maps onto an asymmetric exclusion process involving motion of particles in 1-d with position-dependent right and left jump probabilities. For small ve, the interface is stuck to the field profile. As ve increases the profile detaches from the interface. At the transition point (and beyond), the interfacial structure and dynamics are characterized by the KPZ exponents. For small ve, 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 ve is increased. We determine the dynamical “phase-diagram” of this system in the ve-orientation plane.