  We take advantage of recent improvements in the grand canonical Hybrid Monte
Carlo algorithm, to perform a precision study of the single-particle gap in the
hexagonal Hubbard model, with on-site electron-electron interactions. After
carefully controlled analyses of the Trotter error, the thermodynamic limit,
and finite-size scaling with inverse temperature, we find a critical coupling
of $U_c/\kappa=3.834(14)$ and the critical exponent $z\nu=1.185(43)$. Under the
assumption that this corresponds to the expected anti-ferromagnetic Mott
transition, we are also able to provide a preliminary estimate
$\beta=1.095(37)$ for the critical exponent of the order parameter. We consider
our findings in view of the $SU(2)$ Gross-Neveu, or chiral Heisenberg,
universality class. We also discuss the computational scaling of the Hybrid
Monte Carlo algorithm, and possible extensions of our work to carbon nanotubes,
fullerenes, and topological insulators.
