Abstract
The bilayer spin-2 Ising model on the Bethe lattice is investigated by taking into account the intralayer coupling constants of the two layers J1 and J2, interlayer coupling constant between the layers J3 and crystal field interaction Δ by using the exact recursion equations in a pairwise approach. The ground state (GS) phase diagrams of the model are obtained on the (J2/|J1|, J3/q|J1|) planes for given Δ values and on the (Δ/qJ, J3/qJ) plane when J1 = J2 = J, and thus 33 distinct GS configurations are found. The temperature-dependent phase diagrams are obtained for J1 > 0, J2 > 0, and for J3 > 0 or J3 < 0 on the (kT/J1, J3/J1) planes for given Δ/qJ1 and J2/J1 and on the (Δ/J, kT/J) plane for given J3/J when J1 = J2 = 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.
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