Phase diagram of an Ising model for ultrathin magnetic films:: Comparing mean field and Monte Carlo predictions

We study the critical properties of a two-dimensional Ising model with competing ferromagnetic exchange and dipolar interactions, which models an ultrathin 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 interaction 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. We also found that, in the regions of the phase diagram where Monte Carlo simulations display nematic order, the mean field approximation predicts hybrid solutions composed by stripes of different widths. Another 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.