  In a recent paper [Phys. Rev. {\bf B80}, 174403 (2009)] Kotov {\it et al.}
studied the paramagnetic-to-antiferromagnetic transition in the $J$-$Q$ model.
Their findings were claimed to be in "fairly good agreement" with previous
quantum Monte-Carlo (QMC) results. In this Comment we show that the above claim
is misleading and in reality their phase transition point is not only far from
the corresponding QMC value but also lies in a region of parameter space not
yet explored in the literature. We also show that their reference dimer state
is unstable against formation of a plaquette condensate, which could in part
explain the large fluctuations they found.
