  We provide a unified, comprehensive treatment of all operators that
contribute to the anti-ferromagnetic, ferromagnetic, and charge-density-wave
structure factors and order parameters of the hexagonal Hubbard Model. We use
the Hybrid Monte Carlo algorithm to perform a systematic, carefully controlled
analysis in the temporal Trotter error and of the thermodynamic limit. We
expect our findings to improve the consistency of Monte Carlo determinations of
critical exponents. We perform a data collapse analysis and determine the
critical exponent $\beta=0.898(37)$ for the semimetal-Mott insulator transition
in the hexagonal Hubbard Model. Our methods are applicable to a wide range of
lattice theories of strongly correlated electrons.
