Cubic anisotropic magnets with a random field

The critical behavior at phase transitions of m-component random magnets with cubic anisotropy is studied within the context of an exactly solvable model. The presence of a random field suppresses any phase transition for spatial dimensions d⩽4. If one or more of the components of the random field are zero, but with at least one nonzero component, a new second-order phase transition in the anisotropic phase occurs. In the pure case second-order transitions could happen only into the isotropic phase. The critical temperature of this new, random-field-induced second-order transition decreases with increasing randomness.