The Phase Diagrams of Spin-1/2 Ising Model on a Two-Layer Bethe Lattice with AFM/AFM Interactions

The phase diagrams of spin-1/2 Ising model on a two-layer Bethe lattice with antiferromagnetic interactions for each layer and either antiferromagnetic or ferromagnetic interaction between the layers are investigated by using the pairwise approach for given values of coordination number q. The exact expressions of the order-parameters, response functions and free energy are obtained in terms of the recursion relations. The ground-state phase diagrams are calculated for given system parameters of the model. In the guidance of the ground-state phase diagrams, the temperature dependent phase diagrams of the model are also studied in detail for given coordination numbers q = 3, 4 and 6. It was found that the system presents only second-order phase transitions with different thermal behaviors for all values of q. In addition, two Néel temperatures, $T_{N}$, are found for q = 6 only.