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The phase diagrams of the bilayer spin-(3)/(2) Ising model on the Bethe lattice is analyzed by taking into account the intralayer coupling constants of the two layers (J(1), J(2)), interlayer coupling constant between the layers (J(3)) and crystal field interaction (D) for the coordination number q = 3 by using the exact recursion equations. First, the distinct ground state phase diagrams of the model are obtained on the (J(2)/vertical bar J(1)vertical bar, J(3)/q vertical bar J vertical bar(1)) plane with J(1) > 0 for given crystal field values. Then, the phase diagrams of the system are obtained on the (kT/J(1),J(3)/J(1)) planes for given values of the crystal field and alpha = J(2)/J] on the honeycomb lattice, i.e., q = 3. It was found that the system presents both first- and second-order phase transitions, therefore, tricritical points, and splitting of the critical lines at negative values of the crystal field. The paramagnetic phases are also classified by studying the thermal variations of the quadrupolar moments. (c) 2007 Elsevier B.V. All rights reserved.

The spin-3/2 Ising model on the bilayer Bethe lattice is studied in terms of the exact recursion relations with the intralayer bilinear interactions J(11) and J(22) of the two layers with ferromagnetic coupling and interlayer bilinear interaction J(12) between the layers with ferromagnetic or antiferromagnetic coupling. We first have obtained the ground state configurations of the model on the (J(22)/vertical bar J(11)vertical bar,J(21)q/vertical bar J(11)) planes for J(11)< 0 and J(11)> 0. Then the thermal behaviors of the order-parameters, the total and staggered magnetizations of the two layers and also the spin-spin correlation function between the nearest-neighbor spins of the adjacent layers, are studied to obtain the phase diagrams of the model on the (kT/J(11),J(12)/J(11)) plane for given values of J(22)/J(11) and the coordination number q. As a result, a few types of the critical temperatures of the model are obtained. (c) 2006 Elsevier B.V. All rights reserved.