  Unlike that of SO(3) or SU(2), the Lie algebra for SO(2), which defines
intermediate spin, comprises only $S_{z}$ and implies $S^{\pm}$ commute. In
general, $S_{z}$ has a continuous spectrum. This intermediate spin scheme can
realized for the low energy excitations of a wide class of large spin magnets.
A magnetic field provides the necessary time reversal symmetry breaking and
controls the effective value of the spin $\tilde S$. Physical quantities are
periodic in the equilibrium magnetization component induced by this field. In
particular for one dimensional antiferromagnets there are periodic regions on
the field axis for which the model is quantum critical while in two or three
dimensions criticality is reduced to points.
