$O(n)$ models with “random local field”- and “random local anisotropy”-type defects: Long-range order is possible

Conditions of long-range order breaking in the $O(n)$ model ($n$-component vector model) with “random local field”-type defects have been formulated. It has been suggested that the long-range order can persist in the ground state of the system under certain conditions, despite the emergence of an inhomogeneous state predicted by Imry and Ma in their classical work. Random-local-anisotropy defects cannot destroy the long-range order in the ground state of the system.