We present a theoretical study aimed at elucidating the origin of the inverse symmetry-breaking transition observed in ultrathinmagnetic films with perpendicular anisotropy.We study the behavior of the dipolar frustrated Ising model in a mean field approximation as well as two other models with simple domain walls. By a numerical analysis we show that the internal degrees of freedom of the domain walls are decisive for the presence of the inverse symmetry-breaking transition. In particular, we show that in a sharp domain wall model the inverse transition is absent. At high temperatures the additional degrees of freedom of the extended domain walls increase the entropy of the system leading to a reduction of the free energy of the stripe phase. Upon lowering the temperature the domain walls become narrow, and the reduction of the number of degrees of freedom associated with them manifests in a reduction of entropy which eventually induces an inverse transition to the competing homogenous phase. We also show that, for a growing external field at constant temperature, the stripe width grows strongly when approaching the critical field line and diverges at the transition. These results indicate that the inverse transition is a continuous phase transition and that the domain wall profiles and the temperature have little effect on the critical behavior of the period of the domain as a function of the applied field
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