Cubic anisotropy created by defects of “random local anisotropy” type, and phase diagram of the O(n) Model

The expression for the cubic-type-anisotropy constant created by defects of “random local anisotropy” type is derived. It is shown that the Imry–Ma theorem stating that in space dimensions d < 4 the introduction of an arbitrarily small concentration of defects of the “random local anisotropy” type in a system with continuous symmetry of the n-component vector order parameter (O(n) model) leads to the long-range order collapse and to occurrence of a disordered state, is not true if an anisotropic distribution of the defectinduced random easy axes directions in the order parameter space creates a global anisotropy of the “easy axis” type. For a weakly anisotropic distribution of the easy axes, in space dimensions 2 ≤ d < 4 there exists some critical defect concentration, when exceeded, the inhomogeneous Imry–Ma state can exist as an equilibrium one. At the defect concentration lower than the critical one the long-range order takes place in the system. For a strongly anisotropic distribution of the easy axes, the Imry–Ma state is suppressed completely and the long-range order state takes place at any defect concentration.