  The dielectric constant of multiferroic hexagonal HoMnO_3 exhibits an
unprecedented diversity of anomalies at low temperatures (1.8 K< T <10 K) and
under external magnetic fields related to magnetic phase transitions in the
coupled system of Ho moments, Mn spins, and ferroelectric polarization. The
derived phase diagram is far more complex than previously assumed including
reentrant phases, phase transitions with distinct thermal and field hysteresis,
as well as several multicritical points. Magnetoelastic interactions introduce
lattice anomalies at the magnetic phase transitions. The re-evaluation of the
T-H phase diagram of HoMnO_3 is demanded.
