  Competitive effects of so-called three-site four-spin interactions, single
ion anisotropy and bilinear interactions is studied in the mixed spin-1/2 and
spin-1 Ising model on a decorated square lattice. Exploring the
decoration-iteration transformation, we have obtained exact closed-form
expressions for the partition function and other thermodynamic quantities of
the model. From these relations, we have numerically determined ground- state
and finite-temperature phase diagrams of the system. We have also investigated
temperature variations of the correlation functions, internal energy, entropy,
specific heat and Helmholtz free energy of the system. From the physical point
of view, the most interesting result represents our observation of a partially
ordered ferromagnetic or phase in the system with zero bilinear interactions.
It is remarkable, that due to strong frustrations disordered spins survive in
the system even at zero temperature, so that the ground state of the system
becomes macroscopically degenerate with non-zero entropy. Introduction of
arbitrarily small bilinear interaction completely removes degeneracy and the
entropy always goes to zero at the the ground state.
