The conditions for the appearance in systems with defects of the "random local field" and "random local anisotropy" type of the Imry-Ma phases, in which the direction of the order parameter follows large-scale fluctuations of a random field or random anisotropy, are considered. It is shown that the anisotropy of the distribution of random fields of defects in the space of the order parameter can lead to the appearance of the long-range order. An attention is paid to phase diagrams arising as a result of competition between random fields of defects and anisotropy induced by defects. By the example of a system with random anisotropy (nanocrystalline ferromagnet), the dependences of the coercive field on the crystallite size are considered.
The Hausdorff measure of the range and level sets of Gaussian random fields with sectorial local nondeterminism
