  We address the nature of the antiferromagnetic quantum phase transition that
separates a semimetal from an antiferromagnet in the repulsive Hubbard model
defined on the honeycomb lattice. At the critical point, the fermions acquire
an anomalous dimension $\eta$ due to their strong coupling to the fluctuations
of the order parameter $\phi$. The finite $\eta$ in turn induces a singular
$\phi^{4}$ term and a non-analytical spin susceptibility signaling the
breakdown of Hertz's $\phi^{4}$ theory. As a result, the continuous
antiferromagnetic quantum phase transition is internally unstable and turns
into a first order transition.
