Energy minima and ordering in ferromagnets with static randomness

Energy minimization atT = 0 and Monte Carlo simulations atT > 0 have been performed on 2D and 3D random-field (RF) and random-anisotropy (RA) models of up to 150 million classical spins. The results suggest that 3D RA models magnetically order on lowering temperature, contrary to the theoretical predictions based on the Imry-Ma argument. If RA is weaker than the exchange, the system is free from singularities (hedgehogs in the Heisenberg model and vortex lines in thexymodel). If RA is stronger than the exchange, which can be the case in sintered materials, the system still orders but the magnetization is strongly reduced and there is a large spin-glass component in the spin state, the heat capacity having a cusp instead of a divergence. 3D RF systems do not magnetically order on lowering temperature but rather freeze into the correlated spin-glass state. Here, although magnetized local energy minima have lower energies than non-magnetized ones, magnetic ordering on lowering the temperature is prevented by singularities pinned by the RF.