  We study the effect of a one-dimensional driving field on the interface
between two coexisting phases in a two dimensional model. This is done by
considering an Ising model on a cylinder with Glauber dynamics in all sites and
additional biased Kawasaki dynamics in the central ring. Based on the exact
solution of the two-dimensional Ising model, we are able to compute the phase
diagram of the driven model within a special limit of fast drive and slow spin
flips in the central ring. The model is found to exhibit two phases where the
interface is pinned to the central ring: one in which it fluctuates
symmetrically around the central ring and another where it fluctuates
asymmetrically. In addition, we find a phase where the interface is centered in
the bulk of the system, either below or above the central ring of the cylinder.
In the latter case, the symmetry breaking is `stronger' than that found in
equilibrium when considering a repulsive potential on the central ring. This
equilibrium model is analyzed here by using a restricted solid-on-solid model.
