Abstract
The effects of random field and random anisotropy axis disorder on the two-dimensional $\mathrm{XY}$ dipole ferromagnet are studied. It is shown that the disorder leads to an instability of the ferromagnetic phase. The correlation function of the magnetization is calculated at low temperatures using the self-consistent harmonic approximation. In the random-field case, the correlation function obeys a power law as a function of the distance. For random axis disorder, a logarithmically slow decrease of the correlation function is found.
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