  We study magnetically stabilized nematic order for spin-one bosons in optical
lattices. We show that the Zeeman field-driven quantum transitions between
non-nematic Mott states and quantum spin nematic states in the weak hopping
limit are in the universality class of the ferromagnetic XXZ (S=1/2) spin
model. We further discuss these transitions as condensation of interacting
magnons. The development of O(2) nematic order when external fields are applied
corresponds to condensation of magnons, which breaks a U(1) symmetry.
Microscopically, this results from a coherent superposition of two non-nematic
states at each individual site. Nematic order and spin wave excitations around
critical points are studied and critical behaviors are obtained in a dilute gas
approximation. We also find that spin singlet states are unstable with respect
to quadratic Zeeman effects and Ising nematic order appears in the presence of
any finite quadratic Zeeman coupling. All discussions are carried out for
states in three dimensional bipartite lattices.

Statistical Mechanics