  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.
