  Electrons on the half-filled honeycomb lattice are expected to undergo a
direct continuous transition from the semimetallic into the antiferromagnetic
insulating phase with increase of on-site Hubbard repulsion. We attempt to
further quantify the critical behavior at this quantum phase transition by
means of functional renormalization group (RG), within an effective
Gross-Neveu-Yukawa theory for an SO(3) order parameter ("chiral Heisenberg
universality class"). Our calculation yields an estimate of the critical
exponents $\nu \simeq 1.31$, $\eta_\phi \simeq 1.01$, and $\eta_\Psi \simeq
0.08$, in reasonable agreement with the second-order expansion around the upper
critical dimension. To test the validity of the present method we use the
conventional Gross-Neveu-Yukawa theory with Z(2) order parameter ("chiral Ising
universality class") as a benchmark system. We explicitly show that our
functional RG approximation in the sharp-cutoff scheme becomes one-loop exact
both near the upper as well as the lower critical dimension. Directly in 2+1
dimensions, our chiral-Ising results agree with the best available predictions
from other methods within the single-digit percent range for $\nu$ and
$\eta_\phi$ and the double-digit percent range for $\eta_\Psi$. While one would
expect a similar performance of our approximation in the chiral Heisenberg
universality class, discrepancies with the results of other calculations here
are more significant. Discussion and summary of various approaches is
presented.
