Investigation of thermodynamic properties of the Ising model with pair approximation of cluster variational method

In this study, spin-1 Blume Capel model with anisotropy interaction have been investigated using pair approximation of cluster variational method in the presence of external magnetic field. For that purpose, firstly the pair approximation has been described and applied to spin-1/2 Ising model. Afterwards, the same method has been performed for spin-1 Ising model with bilinear and single-ion anisotropy interactions. The magnetization, quadrupole moment, correlation function, entropy, internal energy and free energy has been obtained by using analtical calculations. The termal variations of order parameters, correlation function, entropy, internal energy, free energy is plotted graphically as a function of temperature and coordination numbers. Finally, both results of lowest and pair approximation have been compared with each other.