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A model consisting of two Bethe lattices each with a branching ratio of q Ising spins with one layer having spin-3/2 with nearest-neighbor (NN) interaction J 1 and crystal field interaction , and the other having spin-1/2 with NN interaction J 2 is considered. The layer with spin-3/2 is laid over the top of the other with spin-1/2 and the two layers are tied together via an interaction between the vertically aligned spins denoted as J 3 . After obtaining the ground state (GS) phase diagrams on different possible planes depending on the given system parameters, the variations of the order-parameters and the free energy are investigated using the exact recursion relations in a pairwise approach to obtain the temperature dependent phase diagrams of the model by considering only the ferromagnetic ordering of the layers, i.e. J 1 > 0 and J 2 > 0, and ferromagnetic or antiferromagnetic ordering of the adjacent NN spins of the layers, J 3 > 0 or J 3 > 0, respectively. Besides the second-order phase transition lines with different kinds of behaviors, the first-order phase transition lines either ending at a tricritical point or at an isolated critical point are found. The model presents compensation temperatures when J 2 of the lower layer can compete with J 1 of the upper layer. The paramagnetic phase is also divided into two phases by studying the thermal behaviors of the quadrupolar moment for the layer with spin-3/2.

The bilayer spin-2 Ising model on the Bethe lattice is investigated by taking into account the intralayer coupling constants of the two layers J 1 and J 2 , interlayer coupling constant between the layers J 3 and crystal field interaction ∆ by using the exact recursion equations in a pairwise approach. The ground state (GS) phase diagrams of the model are obtained on the (J 2 /|J 1 |, J 3 /q|J 1 |) planes for given ∆ values and on the (∆/qJ, J 3 /qJ) plane when J 1 = J 2 = J, and thus 33 distinct GS configurations are found. The temperature-dependent phase diagrams are obtained for J 1 > 0, J 2 > 0, and for J 3 > 0 or J 3 < 0 on the (kT /J 1 , J 3 /J 1 ) planes for given ∆/qJ 1 and J 2 /J 1 and on the (∆/J, kT /J) plane for given J 3 /J when J 1 = J 2 = J for the coordination number q = 3. It was found that the system exhibits both first-and second-order phase transitions and tricritical points. The paramagnetic phases are also classified by studying the thermal variations of the quadrupolar moments. Int. J. Mod. Phys. B 2008.22:4877-4898. Downloaded from www.worldscientific.com by YALE UNIVERSITY on 02/03/15. For personal use only.