  The Hubbard model on the honeycomb lattice undergoes a quantum phase
transition from a semimetallic to a Mott insulating phase and from a disordered
to an anti-ferromagnetically phase. We show that these transitions occur
simultaneously and we calculate the critical coupling $U_c=3.835(14)$ as well
as the critical exponents $\nu=1.181(43)$ and $\beta=0.898(37)$ which are
expected to fall into the $SU(2)$ Gross-Neveu universality class. For this we
employ Hybrid Monte Carlo simulations, extrapolate the single particle gap and
the spin structure factors to the thermodynamic and continuous time limits, and
perform a data collapse fit. We also determine the zero temperature values of
single particle gap and staggered magnetisation on both sides of the phase
transition.

Strongly Correlated Electrons