  Ground-state and finite-temperature behaviour of the mixed spin-1/2 and
spin-1 Ising-Heisenberg model on decorated planar lattices consisting of
inter-connected diamonds is investigated by means of the generalised
decoration-iteration mapping transformation. The obtained exact results clearly
point out that this model has a rather complex ground state composed of two
unusual quantum phases, which is valid regardless of the lattice topology as
well as the spatial dimensionality of the investigated system. It is shown that
the diamond-like decorated planar lattices with a sufficiently high
coordination number may exhibit a striking critical behaviour including
reentrant phase transitions with two or three consecutive critical points.
