Abstract
The ferromagnetic mixed spin- 1 2 and spin- 3 2 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 ( k B T / 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.
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