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Consequences of explicit symmetry breaking in a physically motivated model ofSU(N) antiferromagnet in spatial dimensions one and two are studied. It isshown that the case N=3, which can be realized in spin-1 cold atom systems,displays special properties distinctly different from those for N>=4.Qualitative form of the phase diagram depending on the model parameters isgiven.

Symmetry breaking in low-dimensional SU(N) antiferromagnets