  The transition from topologically nontrivial to a trivial state is studied by
first-principles calculations on bulk zinc-blende type
(Hg$_{1-x}$Zn$_x$)(Te$_{1-x}$S$_x$) disordered alloy series. The random
chemical disorder was treated by means of the Coherent Potential Approximation.
We found that although the phase transition occurs at the strongest disorder
regime (${x\approx 0.5}$), it is still manifested by well-defined Bloch states
forming a clear Dirac cone at the Fermi energy of the bulk disordered material.
The computed residual resistivity tensor confirm the topologically-nontrivial
state of the HgTe-rich (${x<0.5}$), and the trivial state of the ZnS-rich alloy
series (${x>0.5}$) by exhibiting the quantized behavior of the off-diagonal
spin-projected component, independently on the concentration $x$.
