  We report on reentrance in the random field Ising and Blume-Capel models,
induced by an asymmetric bimodal random field distribution. The conventional
continuous line of transitions between the paramagnetic and ferromagnetic
phases, the {\lambda}-line, is wiped away by the asymmetry. The phase diagram,
then, consists of only first order transition lines that always end at ordered
critical points. We find that while for symmetric random field distributions
there was no reentrance, the asymmetry in the random field results in a range
of temperatures for which magnetisation shows reentrance. While this does not
give rise to an inverse transition in the Ising model, for the Blume-Capel
model, however, there is a line of first order inverse phase transitions that
ends at an inverse ordered critical point. We show that the location of the
inverse transitions can be inferred from the ground state phase diagram of the
model.
