In this work we investigate a mixed spin-1/2 and spin-1 Ising model on a decorated square lattice. In addition to standard pair interactions between nearest neighbors, we also consider in our calculations three-site four-spin interactions and the effect of single ion anisotropy. Applying the well-known decoration-iteration transformation, we derive a simple relation between the partition function of the model under investigation and the Onsager's partition function for the simple square lattice. With the help of this mapping relation we are able to calculate exact expressions for all relevant physical quantities of the system (for example, the magnetization, internal energy, Gibbs free energy, entropy and specific heat). The most interesting results have been found in the model without pair interactions. In this case, besides the standard ordered and disordered phases, there also appears an interesting phase which is ordered only partially. Analyzing relevant physical quantities of the system, we have found that the partial ordering is closely related to very strong frustrations that lead to non-zero entropy at T = 0.
