C. Temirci et al., EQUILIBRIUM PROPERTIES OF A SPIN-1 ISING SYSTEM WITH BILINEAR, BIQUADRATIC AND ODD INTERACTIONS, Physica. A, 231(4), 1996, pp. 673-686
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.