IMF2017

After the classical paper by Imry and Ma [PRL 35,1399 (1975)], the viewpoint was firmly established in the literature that at space dimensions d<4 the introduction of an arbitrarily small concentration of defects of the "random local field" or “random easy axis” types into a system with continuous symmetry of the n-component vector order parameter (O(n) model) leads to the long-range order collapse and to the occurrence of a disordered state, which in what follows will be designated as the Imry-Ma state and the statement given above was named the Imry-Ma theorem. We demonstrate that this theorem is not universally true and propose the conditions of its applicability. An anisotropic distribution of the directions of defect-induced random local fields or random easy axes in the order parameter n-dimensional space gives rise to the effective anisotropy in the system. The effective anisotropy can be both “easy axis” and “easy plane” types. The Imry-Ma theorem breaks down due to existence of the “easy axis” anisotropy induced by the defects designed initially for breaking down the long-range order. In the case of slightly anisotropic distribution of the fields or easy axes, there exists a critical concentration of defects, if exceeded, the Imry-Ma inhomogeneous state can exist as an equilibrium one. In the case of strongly anisotropic distribution, the Imry-Ma inhomogeneous state is completely suppressed and the state with the long-range ordering is realized at any defect concentration.