  We study the one-dimensional S=1 Blume-Emery-Griffiths model. Upon
transforming the spin model into an equivalent fermionic model, we provide the
exact solution within the Green's function and equations of motion formalism.
We show that the relevant response functions as well as thermodynamic
quantities can be determined, in the whole parameters space, in terms of a
finite set of local correlators. Furthermore, considering the case of an
antiferromagnetic chain with single-ion anisotropy in the presence of an
external magnetic field, we find three plateaus in the magnetization curve; in
the neighborhood of the endpoints of the intermediate plateau, the specific
heat shows a double peak structure.
