Anisotropy induced by impurities of “random local field” type in $O(n)$ models and suppression of the Imry–Ma inhomogeneous state

It is shown that in a system with anisotropic distribution of the impurity-induced random local field directions in the $n$-dimensional space of a vector order parameter with the $O(n)$ symmetry, the impurityinduced effective anisotropy arises for the space dimensionality 2 $<d<$ 4. If the anisotropy constant exceeds the threshold value, then an inhomogeneous state predicted by Imry and Ma becomes energetically unfavorable, and the system goes back to a state with the long-range order.