H-T phase diagram of the bi-dimensional Ising model with exchange and dipolar interactions

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.