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

The spin-1 Ising model with bilinear (J) and biquadratic (K) interactions is studied for magnetic fields H s and He_) representing dipole and quadrupole moments, respectively, by using the lowest approximation of the cluster variation method. The influence of H s, HQ and a = J/K on metastable and unstable solutions, which are very important for many theoretical and experimental works, is investigated and it is found that metastable and unstable solutions occur at high temperatures when o~ and HQ are increased. However if H s is increased, metastable and unstable solutions can be found only at low temperatures.