  We report numerical investigation of the glassy behavior of random-field
exchange models in three dimensions. Correlation of energy with the
magnetization for different numbers of spin components has been studied. There
is a profound difference between the models with two and three spin components
with respect to the stability of the magnetized state due to the different
kinds of singularities: vortex loops and hedgehogs, respectively. Memory
effects pertinent to such states have been investigated. Insight into the
mechanism of the large-scale disordering is provided by numerically
implementing the Imry-Ma argument in which the spins follow the random field
averaged over correlated volumes. Thermal stability of the magnetized states is
investigated by the Monte Carlo method.
