Crystal field effects on a spin-1 Ising model with AFM-AFM interactions on a two-layer Bethe lattice

Crystal field effects and the influence of changing the coordination numbers q on the phase diagrams of a spin-1 Ising model are investigated for the case of antiferromagnetic (AFM)-AFM interactions on a two-layer Bethe lattice by using the pairwise approach when the layers are linked with the external magnetic fields. The ground state (GS) phase diagrams are calculated on different planes and are used as a guide, together with the free energy and order parameters, to obtain temperature-dependent phase diagrams. It was found that the system gives only one Neel temperature, T(N), for q = 3, but two T(N)'s and reentrant behavior are observed for q = 4 and 6. The first-order phase transitions and tricritical points are also observed for all q with appropriate values of the system parameters. The existence of the crystal field has increased the number of GS configurations and also let the system present first-order phase transitions for q = 3 in comparison with no crystal field.