** Authors:**
Mustafa KESKİN, Hüseyin ARSLAN

** Abstract: **
The spin-1 Ising model [1] with bilinear (J) and biquadratic (K) interactions is
studied for magnetic fields H_S and H_Q representing dipole and quadrupole
moments, respectively, by using the lowest approximation of the cluster
variation method [2]. Thermal variations of stable, metastable and unstable solutions of
the dipole and quadrupole moments as a function of the reduced temperature for
various values of \alpha =J/K. H_S and H_Q are given and discussed in our
previous paper [3], extensively. In this study, we have investigated the effect
of H_S, H_Q and \alpha on metastable and unstable solutions which are very
important for many experimental and theoretical cases, such as metallic glasses,
binary alloys, superfluids, superconductors, gels, lasers, magnetic systems,
astrophysics, glasses and crystalline ceramics, etc. [4]. It is found that
metastable and unstable solutions occur at high temperatures when \alpha and
H_Q are increased. On the other hand, if H_S is increased, metastable and
unstable solutions can be obtained only at low temperatures. The temperature
where the metastable and unstable solutions first exist (while the reduced
temperature is decreasing) is called the quasicritical temperature, T_{qc}.
We also determined that T_{qc} is linear function of \alpha and slopes
are small for small values of H_S and big values of H_Q. Finally, H_S
and H_Q are plotted as a function of T_{qc} and it is found that T_{qc} is
an exponential decaying function of H_S for constant values of \alpha
and H_Q; and T_{qc} is an exponential increasing function of H_Q for constant
values of \alpha and H_S.

** Keywords: **