  We study the critical properties of a two--dimensional Ising model with
competing ferromagnetic exchange and dipolar interactions, which models an
ultra-thin magnetic film with high out--of--plane anisotropy in the monolayer
limit. In this work we present a detailed calculation of the $(\delta,T)$ phase
diagram, $\delta$ being the ratio between exchange and dipolar interactions
intensities. We compare the results of both mean field approximation and Monte
Carlo numerical simulations in the region of low values of $\delta$,
identifying the presence of a recently detected phase with nematic order in
different parts of the phase diagram, besides the well known striped and
tetragonal liquid phases. A remarkable qualitative difference between both
calculations is the absence, in this region of the Monte Carlo phase diagram,
of the temperature dependency of the equilibrium stripe width predicted by the
mean field approximation. We also detected the presence of an increasing number
of metastable striped states as the value of $\delta$ increases.
