A special case of the spin system proposed in the previous paper (i.e. the first paper of this series) is considered, which includes the Heisenberg term besides the four-spin coupling. By means of an improved renormalization within the high density expansion method, the formulas for the temperature-dependent spectra of magnons are obtained, which comprise the whole influence of Gaussian fluctuations of the molecular field. In the whole range of temperature and magnetic field considered the magnon energies are calculated and their jumps at the metamagnetic transition points are established. Existence limits of particular phases are obtained which consequently give the maximum width of a hysteresis loop. A highly interesting thermodynamic phase diagram of the FeBr2 type is derived from our model. The extraordinary behaviour of FeBr2 turns out to follow from the presence of the four-ion term in our model.
