Abstract
Face‐centered‐cubic antiferromagnets with vector spins (including those representing MnO and Cd1−xMnxTe) have nontrivial continuous degeneracies of their ground states which are broken by effects of either thermal or quenched disorder. Using spin‐wave calculations near T=0, it is argued that thermal fluctuations select the collinear states. On the other hand, dilution favors noncollinear (yet long‐range ordered) states.