Ferromagnetism in the mixed spin-12 and spin-32 Blume–Capel system on the two-fold Cayley tree

The ferromagnetic mixed spin-12 and spin-32 Blume–Capel model on the two-fold Cayley tree is investigated using the exact recursion relations. The thermal behavior of magnetizations is studied in detail for different values of the crystal-field interaction Δ and the coordination number q of the sites of the Cayley tree. The exact phase diagrams in the (kBT/J,Δ/J) plane are obtained for different q. The results show that there is no tricritical behavior for the cases of all the coordination numbers and different values of crystal-field interaction. However, there are some interesting phenomena in this system, due to the crystal-field interaction.