Interfaces of Ground States in Ising Models with Periodic Coefficients

We study the interfaces of ground states of ferromagnetic Ising models with external fields. We show that, if the coefficients of the interaction and the magnetic field are periodic, the magnetic field has zero flux over a period and is small enough, then for every plane, we can find a ground state whose interface lies at a bounded distance of the plane. This bound on the width of the interface can be chosen independent of the plane. We also study the average energy of the plane-like interfaces as a function of the direction. We show that there is a well defined thermodynamic limit for the energy of the interface and that it enjoys several convexity properties.