Compensation temperatures, magnetic susceptibilities and phase diagrams of a mixed ferrimagnetic ternary system on the Bethe lattice

Compensation behaviors, magnetic susceptibilities and the phase diagrams of the ternary system of the type $ABC$ consisting of Ising spins $\sigma=1/2$, $S=3/2$ and $m=5/2$ in the presence of a single-ion anisotropy are studied on the Bethe lattice within the framework of the exact recursion relations. Both ferromagnetic and antiferromagnetic exchange interactions are considered. The exact expressions for sublattice magnetizations and magnetic susceptibilities are obtained, and then thermal behaviors of the sublattice magnetizations, total magnetization, magnetic sublattice susceptibilities and total susceptibility are investigated. We find that the system only undergoes a second order phase transition for the different and same bilinear nearest-neighbor exchange interaction parameters, but displays compensation behaviors for only different bilinear interaction parameters. We also present the phase diagrams for the different and same bilinear nearest-neighbor exchange interaction parameters. A comparison is made with the other ternary system of the type $ABC$ consisting of different spin values.