  We have re-analyze the Schwinger boson mean field theory (SBMFT) for
Heisenberg spin models on the cubic lattice. We find that the second order
phase transition point for magnetic ordering previously reported corresponds to
a local maximum of the free energy functional. For both ferromagnetic and
antiferromagnetic Heisenberg models with spin $S \geq S_C$, where $S_C < 1/2$,
the mean field transitions are first order from the magnetically long-ranged
ordered phase to the completely uncorrelated phase. In addition to erroneously
giving a first order transition for magnetic ordering, the mean field theory
does not include a phase with finite short-range correlation, thus negating one
of the prime advantages of SBMFT. The relevance of these pathologies to other
situations beyond the cubic lattice is discussed.
