  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 of the 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.
