Closing relations for the Green's functions of the Heisenberg model with one-ion anisotropy

The spin kinematic relations needed to calculate the magnetization of an anisotropic ferromagnet with arbitrary spin and second-order one-ion anisotropy are established. For a ferromagnet with spin $S=3/2$, the main thermodynamic functions are calculated. It is noted that at low temperatures their behavior is particularly simple because a single spin mode is excited.