±J model on the Bethe lattice with crystal field interaction

Erhan Albayrak, Saban Yilmaz, Seyma Akkaya

James L. Monroe

Erhan Albayrak

A Z Akheyan, N.S. Ananikian

The spin-1 Ising model with bilinear and biquadratic exchange interactions and single-ion crystal field is solved on the Bethe lattice using exact recursion equations. The general procedure of critical properties investigation is discussed and full set of phase diagrams are constructed for both positive and negative biquadratic couplings. In latter case we observe all remarkable features of the model, uncluding doubly-reentrant behavior and ferrimagnetic phase. A comparison with the results of other approximation schemes is done.

A.R. Avakian, N. S. Ananikyan, N. Sh. Izmailian

Osman Canko, Erhan Albayrak

The influence of the crystal field on the phase diagrams of the bilayer spin-1 Ising model on the Bethe lattice is studied in terms of the intralayer coupling constants J1 and J2 of the two layers and interlayer coupling constant J3 between the layers for given values of the coordination number q by using the recursion relation scheme. The six distinct ground-state configurations of the model are obtained on the (J_{2}J_{1},J_{3}qJ_{1}) plane with J1>0 , the ferromagnetic coupling, for given values of the crystal field. Then, the phase diagram of the system is obtained on the (kTJ_{1},J_{3}J_{1}) plane for given values of the crystal field and alpha=J_{2}J_{1} with q=4 corresponding to the square lattice in real lattice systems. It was found that the system presents both first- and second-order phase transitions, therefore, tricritical points. The paramagnetic phase was also divided into two phases, P+ and P_{-} , by studying the thermal behavior of the quadrupolar moments of the two layers.