  The generalized Fisher super-exchange antiferromagnetic model with uniaxial
crystal-field anisotropy is exactly investigated using an extended mapping
technique. An exact relation between partition function of the studied system
and that one of the standard zero-field spin-1/2 Ising model on the
corresponding lattice is obtained applying the decoration-iteration
transformation. Consequently, exact results for all physical quantities are
derived for arbitrary spin values S of decorating atoms. Particular attention
is paid to the investigation of the effect of crystal-field anisotropy and
external longitudinal magnetic field on magnetic properties of the system under
investigation. The most interesting numerical results for ground-state and
finite-temperature phase diagrams, thermal dependences of the sublattice
magnetization and other thermodynamic quantities are discussed.
