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The influence of defects of the "random local field" type with an anisotropicdistribution of random fields on two-dimensional models with continuoussymmetry of the vector order parameter is considered. In the case of weakanisotropy of random fields, with decreasing temperature there takes place asmooth transition from the paramagnetic phase with dynamic fluctuations of theorder parameter to the Imry-Ma phase with static fluctuations caused byfluctuations of the random field of defects. In the case of strong anisotropyof random fields, defects lead to an effective decrease in the number ofcomponents of the order parameter and the appearance of a phase transition toan ordered state at finite temperature. It is shown that in the case of thedefect-free two-dimensional X-Y model, the appearance of an arbitrarily weakanisotropy in the two-dimensional space of the order parameter completelyeliminates the appearance of the Berezinsky-Kosterlitz-Thouless phase and givesrise to the phase with the long-range order.

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