  The mixed spin-(1/2, 3/2) Ising model on a decorated square lattice, which
takes into account lattice vibrations of the spin-3/2 decorating magnetic ions
at a quantum-mechanical level under the assumption of a perfect lattice
rigidity of the spin-1/2 nodal magnetic ions, is examined via an exact mapping
correspondence with the effective spin-1/2 Ising model on a square lattice.
Although the considered magnetic structure is in principle unfrustrated due to
bipartite nature of a decorated square lattice, the model under investigation
may display anomalous spin frustration driven by a magnetoelastic coupling. It
turns out that the magnetoelastic coupling is a primary cause for existence of
the frustrated antiferromagnetic phases, which exhibit a peculiar coexistence
of antiferromagnetic long-range order of the nodal spins with a partial
disorder of the decorating spins with possible reentrant critical behaviour.
Under certain conditions, the anomalous spin frustration caused by the
magnetoelastic coupling is responsible for unprecedented absence of spontaneous
long-range order in the mixed-spin Ising model composed from half-odd-integer
spins only.
