  We investigate ground state and finite temperature properties of the
half-filled Hubbard model on a honeycomb lattice using quantum monte carlo and
series expansion techniques. Unlike the square lattice, for which magnetic
order exists at T=0 for any non-zero $U$, the honeycomb lattice is known to
have a semi-metal phase at small $U$ and an antiferromagnetic one at large $U$.
We investigate the phase transition at T=0 by studying the magnetic
structure$and compressibility using quantum monte carlo simulations and by
calculating the sublattice magnetization, uniform susceptibility, spin-wave and
single hole %single-particle dispersion using series expansions around the
ordered phase. Our results are consistent with a single continuous transition
at $U_c/t$ in the range 4-5. Finite temperature signatures of this phase
transition are seen in the behavior of the specific heat, $C(T)$, which changes
from a two-peaked structure for $U>U_c$ to a one-peaked structure for $U <
U_c$. Furthermore, the $U$ dependence of the low temperature coefficient of
$C(T)$ exhibits an anomaly at $U \approx U_c$.
