EQUILIBRIUM PROPERTIES OF A SPIN-1 ISING SYSTEM WITH BILINEAR, BIQUADRATIC AND ODD INTERACTIONS

The equilibrium properties of the spin-1 Ising system Hamiltonian with arbitrary bilinear (J), biquadratic (K) and odd (L), which is also ca lled dipolar-quadrupolar, interactions is studied for zero magnetic fi eld in the lowest approximation of the cluster variation method. The o dd interaction is combined with the bilinear (dipolar) and biquadratic (quadrupolar) exchange interactions by the geometric mean. In this sy stem, phase transitions depend on the ratio of the coupling parameters , alpha = J/K; therefore, the dependence of the nature of the phase tr ansition on alpha is investigated extensively and it is found that for alpha less than or equal to 1 and alpha greater than or equal to 2000 a second-order phase transition occurs, and for 1 < alpha < 2000 a fi rst-order phase transition occurs. The critical temperatures in the ca se of a second-order phase transition and the upper and lower limits o f stability temperature in the case of a first-order phase transition are obtained for different values of alpha calculated using the Hessia n determinant. The first-order phase transition temperatures are found by using the free energy values while increasing and decreasing the t emperature. Besides the stable branches of the order parameters, we es tablish also the metastable and unstable parts of these curves and the thermal variations of these solutions as a function of the reduced te mperature are investigated. The unstable solutions for the first-order phase transitions are obtained by displaying the free energy surfaces in the form of a contour map. Results are compared with the spin-1 Is ing system Hamiltonian with the bilinear and biquadratic interactions and it is found that the odd interaction greatly influences the phase transitions.