  We present a numerical study of the spin Hall effect in a two-dimensional
hole gas (2DHG) system in the presence of disorder. We find that the spin Hall
conductance (SHC), extrapolated to the thermodynamic limit, remains finite in a
wide range of disorder strengths for a closed system on torus. But there is no
intrinsic spin Hall accumulation as induced by an external electric field once
the disorder is turned on. The latter is examined by performing a Laughlin's
Gedanken gauge experiment numerically with the adiabatical insertion of a flux
quantum in a belt-shaped sample, in which the absence of level crossing is
found under the disorder effect. Without disorder, on the other hand, energy
levels do cross each other, which results in an oscillating
spin-density-modulation at the sample boundary after the insertion of one flux
quantum in the belt-shaped system. But the corresponding net spin transfer is
only about one order of magnitude smaller than what is expected from the bulk
SHC. These apparently contradictory results can be attributed to the violation
of the spin conservation law in such a system. We also briefly address the
dissipative Fermi surface contribution to spin polarization, which may be
relevant to experimental measurements.
