  Taking into account both random impurity distribution and thermal
fluctuations of localized spins, we have performed a model calculation for the
carrier (hole) state in Ga$_{1-x}$Mn$_x$As by using the coherent potential
approximation (CPA). The result reveals that a {\it p}-hole in the band tail of
Ga$_{1-x}$Mn$_x$As is not like a free carrier but is rather virtually bounded
to impurity sites. The carrier spin strongly couples to the localized {\it d}
spins on Mn ions. The hopping of the carrier among Mn sites causes the
ferromagnetic ordering of the localized spins through the double-exchange
mechanism. The Curie temperature obtained by using conventional parameters
agrees well with the experimental result.
