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Inverse transition in the two dimensional dipolar frustrated ferromagnet

We show that the mean field phase diagram of the dipolar frustrated ferromagnet in an external field presents an inverse transition in the field-temperature plane. The presence of this type of transition has recently been observed experimentally in ultrathin films of Fe/Cu(001). We study a coarse-grained model Hamiltonian in two dimensions. The model supports stripe and bubble equilibrium phases, as well as the paramagnetic phase. At variance with common expectations, already in a single mode approximation, the model shows a sequence of paramagnetic-bubbles-stripes-paramagnetic phase transitions upon lowering the temperature at fixed external field. Going beyond the single mode approximation leads to the shrinking of the bubbles phase, which is restricted to a small region near the zero field critical temperature. Monte Carlo simulations results with a Heisenberg model are consistent with the mean field results.