Imry–Ma disordered state induced by impurities of “random local anisotropy” type in the system with $O(n)$ symmetry

For the system with the $n$-component order parameter ($O(n)$-model), conditions for initiation of the Imry–Ma disordered state resulting from the influence of impurities of the “random local anisotropy” type were discovered. The initiation of such a state was shown to be possible if the distribution of local anisotropy axes directions in the order parameter space is nearly isotropic, and the limiting degree of the distribution anisotropy was found. For a higher anisotropy in the distribution of local axes directions, the long-range order in the system holds true even in the presence of impurities of the given type.