  We study the ground state properties of kinetic-exchange models for (III,Mn)V
semiconductors with randomly distributed Mn ions. Our method is embedded in a
path integral spin-wave type formalism leading to an effective action for Mn
spins only with full Matsubara frequency dependence. The zero-frequency
contribution to this action is equivalent to static perturbation theory and
characterizes the stabilty of a given spin configuration, while the component
linear in frequency can be interpreted as the joint Berry phase of the Mn and
carrier system. For simple parabolic-band carriers the collinear ferromagnetic
state with all Mn spins in parallel is always stationary but generically
unstable. This instability can be characterized in terms of inverse
participation ratios and is due to long-ranged nonlocal spin fluctuations. We
also present results for the ground state magnetization as a function of an
external field. For carrier dispersions involving anisotropy induced by
spin-orbit coupling the collinear state is not even stationary and therefore
also not the ground state. This interplay between the anisotropy in the carrier
system and the disorder in the Mn positions reflects recent findings by Zarand
and Janko (Phys. Rev. Lett. 89, 047201 (2002)) obtained within the RKKY
approximation. The stationarity of the collinear state (with the magnetization
pointing in one of the cubic symmetry directions) is restored in the continuum
or virtual crystal approximation where disorder is neglected.
