Weak disorder in a two-dimensional dipole magnet

The effect of "random-field" disorder and "random-anisotropy-axis" disorder on a two-dimensional dipole ferromagnet is investigated. It is shown that disorder results in instability of the ferromagnetic phase. The correlation function of the magnetization is calculated with the aid of a self-consistent harmonic approximation. It is found that in the presence of a random field the correlation function is a power-law function of the distance. In the presence of random anisotropy the correlation function decreases logarithmically slowly as a function of distance.