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The mixed spin-(1/2, 3/2) Ising model on a decorated square lattice, whichtakes into account lattice vibrations of the spin-3/2 decorating magnetic ionsat a quantum-mechanical level under the assumption of a perfect latticerigidity of the spin-1/2 nodal magnetic ions, is examined via an exact mappingcorrespondence with the effective spin-1/2 Ising model on a square lattice.Although the considered magnetic structure is in principle unfrustrated due tobipartite nature of a decorated square lattice, the model under investigationmay display anomalous spin frustration driven by a magnetoelastic coupling. Itturns out that the magnetoelastic coupling is a primary cause for existence ofthe frustrated antiferromagnetic phases, which exhibit a peculiar coexistenceof antiferromagnetic long-range order of the nodal spins with a partialdisorder of the decorating spins with possible reentrant critical behaviour.Under certain conditions, the anomalous spin frustration caused by themagnetoelastic coupling is responsible for unprecedented absence of spontaneouslong-range order in the mixed-spin Ising model composed from half-odd-integerspins only.

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Absence of a spontaneous long-range order in a mixed spin-(1/2, 3/2)  Ising model on a decorated square lattice due to anomalous spin frustration  driven by a magnetoelastic coupling