  Mean-field-theory predicts that the Curie temperature T_c of a (III,Mn)V
ferromagnet will be proportional to the valence band density-of-states of its
host (III,V) semiconductor, suggesting a route toward room-temperature
ferromagnetism in this materials class. In this Letter, we use theoretical
estimates of spin-wave energies and Monte-Carlo simulations to demonstrate that
long-wavelength collective fluctuations, neglected by mean-field theory, will
limit the critical temperature in large density-of-states materials. We discuss
implications for high T_c searches.
