  We explore the equilibrium properties of a two-dimensional Ising spin model
with short-range exchange and long-range dipolar interactions as a function of
the applied magnetic field H. The model is studied through extensive Monte
Carlo simulations that show the existence of many modulated phases with long
range orientational order for a wide range of fields. These phases are
characterized by different wave vectors that change discontinuously with the
magnetic field. We provide numerical evidence supporting the existence of first
order transitions between these phases. At higher fields our results suggest a
Kosterliz-Thouless scenario for the transition from a bubble to a ferromagnetic
phase.
