A study of the bilayer Bethe lattice for spin-32 Ising model

The spin-32 Ising model on the bilayer Bethe lattice is studied in terms of the exact recursion relations with the intralayer bilinear interactions J11J11 and J22J22 of the two layers with ferromagnetic coupling and interlayer bilinear interaction J12J12 between the layers with ferromagnetic or antiferromagnetic coupling. We first have obtained the ground state configurations of the model on the (J22/|J11|,J12/q|J11|)(J22/|J11|,J12/q|J11|) planes for J11<0J11<0 and J11>0J11>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/J11,J12/J11)(kT/J11,J12/J11) plane for given values of J22/J11J22/J11 and the coordination number qq. As a result, a few types of the critical temperatures of the model are obtained.