Stable, metastable and unstable solutions of a spin-1 Ising system in the presence of magnetic fields due to the dipole and quadrupole moments

Özet

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 a on metastable and unstable solutions which are very important for many experimental and theoretical cases, such as metallic glasses, binary alloys, superfiuids, 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 a 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 a 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 a and $H_Q$ ; and $T_{qc}$ is an exponential increasing function of $H_Q$ for constant values of a and $H_S$.