  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. It is shown that in the case of the
defect-free two-dimensional X-Y model, the appearance of an arbitrarily weak
anisotropy in the two-dimensional space of the order parameter completely
eliminates the appearance of the Berezinsky-Kosterlitz-Thouless phase and gives
rise to the phase with the long-range order.
