  Using determinant Quantum Monte Carlo, we compare three methods of evaluating
the DC Hall coefficient $R_H$ of the Hubbard model: the direct measurement of
the off-diagonal current-current correlator $\chi_{xy}$ in a system coupled to
a finite magnetic field (FF), $\chi_{xy}^{\text{FF}}$; the three-current linear
response to an infinitesimal field as measured in the zero-field (ZF) Hubbard
Hamiltonian, $\chi_{xy}^{\text{ZF}}$; and the leading order recurrent expansion
$R_H^{(0)}$ in terms of thermodynamic susceptibilities. The two quantities
$\chi_{xy}^{\text{FF}}$ and $\chi_{xy}^{\text{ZF}}$ can be compared directly in
imaginary time. Proxies for $R_H$ constructed from the three-current correlator
$\chi_{xy}^{\text{ZF}}$ can be determined under different simplifying
assumptions and compared with $R_H^{(0)}$. We find these different quantities
to be consistent with one another, validating previous conclusions about the
close correspondence between Fermi surface topology and the sign of $R_H$, even
for strongly correlated systems. These various quantities also provide a useful
set of numerical tools for testing theoretical predictions about the full
behavior of the Hall conductivity for strong correlations.
