  The spin-1 Ising model with bilinear and quadrupolar short-range interactions
under magnetic field is investigated within the two-particle cluster
approximation. It is shown that for those values of the quadrupolar interaction
when at zero magnetic field the system undergoes a temperature phase transition
between quadrupolar and paramagnetic phases, a triple point may exist in the
temperature vs magnetic field phase diagrams, necessarily along with a critical
point. It is also shown that the critical points in the temperature vs magnetic
field phase diagrams of the investigated model can be of three types.
