The effect of uniaxial crystal-field anisotropy on magnetic properties of the superexchange antiferromagnetic Ising model

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 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.