Pair correlation functions of the Ising type model with spin 1 within two-particle cluster approximation

The Blume-Emery-Griffiths model on hypercubic lattices within the two-particle cluster approximation is investigated. The expressions for the pair correlation functions in $\mathbf{k}$-space are derived. On the basis of obtained results (at $\mathbf{k}=\mathbf{0}$) the static susceptibility of this model on the simple cubic lattice is calculated at various values of the single-ion anisotropy and biquadratic interaction.