  Motivated by experiments on NiGa2S4, we discuss characteristic (finite
temperature) properties of spin S = 1 quantum antiferromagnets on the
triangular lattice. Several recent theoretical studies have suggested the
possibility of quadrupolar (spin-nematic) ground states in the presence of
sufficient biquadratic exchange. We argue that quadrupolar correlations are
substantially more robust than the spin-nematic ground state, and give rise to
a two peak structure of the specific heat. We characterize this behavior by a
novel T > 0 semiclassical approximation, which is amenable to efficient Monte
Carlo simulations. Turning to low temperatures, we consider the effects of weak
disorder on incommensurate magnetic order, which is present when interactions
beyond nearest neighbor exchange are substantial. We show that non-magnetic
impurities act as random fields on a component of the order parameter, leading
to the disruption of long-range magnetic order even when the defects are
arbitrarily weak. Instead, a gradual freezing phenomena is expected on lowering
the temperature, with no sharp transition but a rapid slowing of dynamics and
the development of substantial spin-glass-like correlations. We discuss these
observations in relation to measurements of NiGa2S4.
