  We report the observation of an unexpected quadratic temperature dependence
of the heat capacity in the vanadium sulphide metal V5S8 at low temperatures
which is independent of applied magnetic field. We find that the behaviour of
the heat capacity is consistent with an unconventional phonon spectrum which is
linear in wavevector in the c direction but quadratic in the a-b plane,
indicating a form of geometrical elastic criticality. In the case of V5S8 we
also observe an unusual intermediate transition at high magnetic fields between
the expected spin-flop and spin-flip transitions. We demonstrate that the
intermediate field-induced transition is in agreement with a model of two
sublattices with frustrated inter- and intra-sublattice spin couplings.
