Mixed and Blume–Capel Ising ferrimagnetic system on the Bethe lattice

We present the exact formulation for the mixed and Blume–Capel Ising ferrimagnetic system on the Bethe lattice by the use of exact recursion relations. The exact expressions for the magnetization, quadrupole moment, Curie temperature and free energy are found and the phase diagrams are illustrated on the Bethe lattice with the coordination numbers q=3, 4, 5 and 6. It is found that the phase diagram of this mixed spin system only presents second-order phase transitions. The thermal variation of the magnetization belonging to each sublattice and the net magnetization are also presented.