Magnetic properties of the spin-1 Blume-Emery-Griffiths model in the presence of magnetic field

Magnetic properties of the spin-1 Blume-Capel (BC) model and Blume-Emery-Griffiths (BEG) model on square lattice are presented within the framework of the effective-field theory (EFT) with correlations approximation method and Monte Carlo simulation technique. We have improved the EFT method by including the correlations between different spins which emerge when expanding the identities. In order to do this, we have derived a set of linear equations for the considered systems by taking as a basis the thermal averages of a central spin and a perimeter spin at the site i, which is defined within the spin identities and differential operator technique. By solving numerically the set of linear equations derived for the Ising system with coordination number q=4, we have evaluated all the spin correlation functions without using any kind of decoupling approximation in the spin system under a longitudinal magnetic field. The effects of the longitudinal magnetic field on magnetic properties of the spin systems are discussed in detail. Numerical computations are performed and the results are analyzed for the cases of the spin-1 BC model by using effective-field theory with correlations and spin-1 BEG model by applying Monte Carlo simulations on the square lattice, respectively. We have also evaluated the phase diagrams for the spin-1 BC model on square lattice