Mixed Spin-1 and Spin-3/2 BC Ferromagnetic System On the Two-fold Cayley Tree

The mixed spin-1 and spin -3/2 BC Ising ferromagnetic system is studied on the two -fold Cayley tree by means of the exact recursion relations. The exact expressions for the magnetization, the quadripolar moment, the Curie temperature, and the free energy are found, and the phase diagrams are constructed on the Cayley tree with the coordination numbers q = 3, 4 and 6 for various values of the single-ion anisotropy constants Delta(1) = D1/J for spin-1 and Delta(2) = D2/J for spin-3/2. The existence of tricritical point is investigated for different values of the coordination numbers q and the single-ion anisotropy values. Phase diagrams in the plan (kT / J, Delta(1)) are constructed when first Delta(1)= Delta(2) and second Delta(1) not equal Delta(2) for selected values of Delta(2). The thermal dependence of the magnetization is also studied. The results found are compared with those of other approximate methods.