Dzyaloshinskii-Moriya interaction and magnetic ordering in 1D and 2D at nonzero $T$

The inclusion of a Dzyaloshinskii-Moriya short range antisymmetric interaction induces spontaneous magnetization, at nonzero temperatures, in one and two dimensions. It is shown that quantum fluctuations are reduced by the Dzyaloshinskii-Moriya interaction, but short range correlations are increased, thereby allowing to obtain long range magnetic order in these low dimensional systems.