Ferromagnetism in the Blume-Emery-Griffiths model on finite-size Cayley tree

The ferromagnetic properties of the spin-1 BEG model on finite-size Cayley tree are investigated using the exact recursion method. The spontaneous magnetization of the system is studied in detail for different values of the reduced crystal-field interaction D/J, and it is found that there is an unusual behavior (anti-Curie temperature) when D/J>2.0. We also obtain the Curie temperature of this finite-size system. When the system size is large enough, our results will fit well with that in the thermodynamic limit.