  Monte Carlo simulations, in which the Schrodinger equation is solved at each
Monte Carlo sweep, are employed to assess the influence of magnetization
fluctuations,short-range antiferromagnetic interactions, disorder, magnetic
polaron formation, and spin-Peierls instability on the carrier-mediated Ising
ferromagnetism in two-dimensional electronic systems. The determined critical
temperature and hysteresis are affected in a nontrivial way by the
antiferromagnetic interactions. The findings explain striking experimental
results for modulation-doped p-CdMnTe quantum wells.
