  We use Quantum Monte Carlo methods to determine $T=0$ Green functions,
$G(\vec{r}, \omega)$, on lattices up to $16 \times 16$ for the 2D Hubbard model
at $U/t =4$. For chemical potentials, $\mu$, within the Hubbard gap, $ |\mu | <
\mu_c$, and at {\it long} distances, $\vec{r}$, $G(\vec{r}, \omega = \mu) \sim
e^{ -|\vec{r}|/\xi_l}$ with critical behavior: $\xi_l \sim | \mu - \mu_c
|^{-\nu}$, $ \nu = 0.26 \pm 0.05$. This result stands in agreement with the
assumption of hyperscaling with correlation exponent $\nu = 1/4$ and dynamical
exponent $z = 4$. In contrast, the generic band insulator as well as the
metal-insulator transition in the 1D Hubbard model are characterized by $\nu =
1/2$ and $z = 2$.
