Comment on "Polar and antiferromagnetic order in f=1 boson systems"
  An inequality for the lower bound of the average number of hyperfine component $\mu =0$ particles in the ground state of spin-1 condensates under a magnetic field has been derived in ref.\cite{tasa13}. It is shown in this comment that, in a broad domain of parameters usually accessed in experiments, the lower bound appears to be negative.   Thus the applicability of the inequality is very limited. 
C.G. Bao
cond-mat.quant-gas quant-ph