  The magnetic phases of hexagonal perovskites RMnO_3 (R=Ho, Er, Tm, Yb, Sc, Y)
are analysed using group theory and the Landau theory of phase transitions. The
competition between various magnetic order parameters is discussed in the
context of antiferromagnetic interactions. A phenomenological model based on
four one-dimensional magnetic order parameters is developed and studied
numerically. It is shown that coupling of the various order parameters leads to
a complex magnetic field-temperature phase diagram and the results are compared
to experiment.
