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

TL;DR

This paper investigates the behavior of a 2D Ising interface under an inhomogeneous moving external field, revealing phase transitions, interface detachment, and KPZ scaling in the system's steady states and dynamics.

Contribution

It introduces a novel analysis of interface dynamics in a 2D Ising model with a moving field, connecting microscopic interface behavior to KPZ universality and phase transitions.

Findings

Interface remains stuck at low field velocities.

Interface detaches and exhibits KPZ scaling at higher velocities.

A phase diagram maps the interface behavior across velocities and orientations.

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 $\alpha$. 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.