Pathology of Schwinger boson mean-field theory for Heisenberg spin models

We reanalyze 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 ≥ 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.