  We report on a comparative numerical study of the spin Hall conductivity in
two-dimensions for three different spin-orbit interaction models; the standard
k-linear Rashba model, the k-cubic Rashba model that describes two-dimensional
hole systems, and a modified k-linear Rashba model in which the spin-orbit
coupling strength is energy dependent. Numerical finite-size Kubo formula
results indicate that the spin Hall conductivity of the k-linear Rashba model
vanishes for frequency $\omega$ much smaller than the scattering rate
$\tau^{-1}$, with order one relative fluctuations surviving out to large system
sizes. For the k-cubic Rashba model case, the spin Hall conductivity does not
depend noticeably on $\omega \tau$ and is finite in the {\em dc} limit, in
agreement with experiment. For the modified k-linear Rashba model the spin Hall
conductivity is noticeably $\omega \tau$ dependent but approaches a finite
value in the {\em dc} limit. We discuss these results in the light of a
spectral decomposition of the spin Hall conductivity and associated sum rules,
and in relation to a proposed separation of the spin Hall conductivity into
skew-scattering, intrinsic, and interband vertex correction contributions.
