  We analyze the quantum phase transition between a semimetal and a superfluid
in a model of attractively interacting fermions with a linear dispersion. The
quantum critical properties of this model cannot be treated by the Hertz-Millis
approach since integrating out the fermions leads to a singular Landau-Ginzburg
order parameter functional. We therefore derive and solve coupled
renormalization group equations for the fermionic degrees of freedom and the
bosonic order parameter fluctuations. In two spatial dimensions, fermions and
bosons acquire anomalous scaling dimensions at the quantum critical point,
associated with non-Fermi liquid behavior and non-Gaussian order parameter
fluctuations.
