Nature of a phase transition and low-temperature phase in cubic ferromagnets

A S=2 ferromagnet with a crystalline field of the cubic symmetry is studied. It is shown that ill the case of the three easy axes [100] the model which contains only the Heisenberg bilinear interaction and single-ion anisotropy terms exhibits at a finite temperature the phase transition to a nonmagnetic phase with a long-range quadrupolar order. It is also pointed out if the recent result that in three dimensions the cubic fixed point is stable for the (n=3)-component cubic spin model (Kleinert, Thorns, and Schulte-Frohlinde) is correct, all cubic ferromagnets with three easy axes, for example Fe, should undergo a first-order (discontinuous) phase transition. [S0163-1829(99)02806-4].