The Study Of Thermodynamic Properties Of The Blume-Emery-Griffiths Model On Cayley Tree

Recently, the Blume-Capel model and Blume-Emery-Griffiths model have received a great deal of attention. Using the exact recursion method, the thermodynamic behavior of the above two models on finite-size Cayley tree is studied. The main results are given as follows:For the Blume-Capel system, the effects of the crystal-field interaction on the thermo-dynamic behavior of the system are investigated for the ferromagnetic case. In the case of the coordination number q=4 and generation number n=16, the spontaneous magnetization and zero field susceptibility with temperature are obtained by numerical calculation. It is shown that the magnetization curves exhibit some unusual features including an anti-Curie temperature. As the crystal-field interaction decreases, the anti-Curie temperature drops to lower value and vanishes finally while the maximum magnetization of curves increases and approaches to unity at zero temperature. The tendency of the curves agrees with the case in the thermodynamic limit. The zero field susceptibility curves tend to infinity at the critical temperature in the thermodynamic limit. The results show that there exists a two-order transition.For the Blume-Emey-Griffiths system, the spontaneous magnetization is calculated in detail for different values of the reduced crystal-field interaction. The results show that the unusual behavior of the magnetization occurs when the variable is greater than a certain value. Besides the anti-Curie temperature, the phase transition temperature is obtained from the magnetization curve. Then, we also present magnetization with temperature for different coordination numbers and generation numbers. When the system size is large enough, the results will fit well with that in the thermodynamic limit. Besides, the spontaneous magnetization of the system is calculated for varied values of the biquadratic interaction and the same variation range of the reduced crystal-field interaction used above. The results show that as the increase of the biquadratic interaction value, the spontaneous magnetization curve tends to the conventional curve, and the anti-Curie temperature disappears.