Transfer matris metodunun bilineer ve bikuadratik değişme etkileşmeli Hamiltoniyene sahip spin-1 Ising modeline uygulanması

Transfer matris metodu, bilineer (J) ve bikuadratik (K) değişim etkileşme Hamiltoniyenine sahip spin-1 Ising modeline magnetik alan yokluğunda uygulandı. Spin-1 Ising modelinin moleküler alan yaklaşımıyla incelenmesine alternatif olarak, transfer matris metodu ele alındı. Transfer matris metodunda düzen parametresi olan kuadrupol moment (Q) sıcaklığın fonksiyonu olarak bulundu. Bunun sonucu; Q' nun kararlı çözümleri elde edilip, faz geçişleri belirlendi. Anizotropinin $(frac{Delta}{K})$ değişimine bağlı kuadrupol moment Q' nun sıcaklığa bağlı olarak değiştiği görüldü. Transfer matris metoduyla elde edilen kuadrupol düzen parametresinin sıcaklığa bağlı kararlı çözümlerinin, moleküler alan yaklaşımıyla elde edilen kararlı çözümlerle uygunluğu belirlendi.

The application of transfer matrix method to spin-1 Ising model having Hamiltonian with bilinear and biquadratic variation interaction

The transfer matrix method has been applied to spin-1 Ising model having Hamiltonian with bilinear (J) and biquadratic (K) variation interaction in the absence of magnetic field. Transfer matrix method has been considered as an alternative to examining the Ising model with molecular field approximation. The quadrupol moment (Q) being order parameter in the transfer matrix method has been found to be the function of temperature. As a result, stable solutions of Q have been obtained and phase transitions have been determined. It has been found that the quadrupol moment Q varies with the temperature, depending of the variation of the anisotropy $(frac{Delta}{K})$. Temperature dependent stable solutions of quadrupol order parameter obtained by transfer matrix method has been determined to agree with stable solutions obtained by molecular field approximation.

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