Long-range order induced by random fields in two-dimensional $O(n)$ models, and the Imry–Ma state

The influence of defects of the “random local field” type with an anisotropic distribution of random fields on two-dimensional models with continuous symmetry of the vector order parameter is considered. In the case of weak anisotropy of random fields, with decreasing temperature there takes place a smooth transition from the paramagnetic phase with dynamic fluctuations of the order parameter to the Imry–Ma phase with static fluctuations caused by fluctuations of the random field of defects. In the case of strong anisotropy of random fields, defects lead to an effective decrease in the number of components of the order parameter and the appearance of a phase transition to an ordered state at finite temperature.