The Crystal Field Effects in the Spin-1 ising Model with FM/AFM Interactions on a Two-layer Bethe Lattice

摘要

The exact recursion equations in a pair-wise approach are used to study the phase transitionson a two-layer Bethe lattice with crystal field (D) and external magnetic field (H) acting on thelayers. The ferromagnetic (FM) and the antiferromagnetic (AFM) interactions for the spins of theupper and the lower layers, respectively, and either a FM- or an AFM-type interaction betweenthe adjacent spins of the layers are assumed. The ground state (GS) phase diagrams of the modelare calculated on the (J_2/ J_1, 3/ qJ_1)planes for given system parameters, and thirteen distinctGS configurations are obtained. With the GS phase diagrams, the temperature-dependent phasediagrams of the model are obtained by studying the thermal behaviors of the order parameters andthe response functions. The model was found to exhibit first- and second-order phase transitionsfor the coordination numbers q = 3, 4, and 6; hence, tricritical points are also observed. A reentrantbehavior is also found whenever the model displays two Neel temperatures.