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Ultrathin magnetic films can be modeled as an anisotropic Heisenberg modelwith long-range dipolar interactions. It is believed that the phase diagrampresents three phases: An ordered ferromagnetic phase I, a phase characterizedby a change from out-of-plane to in-plane in the magnetization II, and ahigh-temperature paramagnetic phase III. It is claimed that the border linesfrom phase I to III and II to III are of second order and from I to II is firstorder. In the present work we have performed a very careful Monte Carlosimulation of the model. Our results strongly support that the line separatingphases II and III is of the BKT type.

Phase transition in ultrathin magnetic films with long-range interactions: Monte Carlo simulation of the anisotropic Heisenberg model