We investigate the effect of geometrical frustration on the H-T phase diagrams of the classical Heisenberg antiferromagnets on triangular and kagome lattices. The phase diagrams for the two models are obtained from large-scale Monte Carlo simulations. For the kagome antiferromagnet, thermal fluctuations are unable to lift degeneracy completely and stabilize translationally disordered multipolar phases. We find a substantial difference in the temperature scales of the order by disorder effect related to different degeneracy of the low- and the high-field classical ground states in the kagome antiferromagnet. In the low-field regime, the Kosterlitz-Thouless transition into a spin-nematic phase is produced by unbinding of half-quantum vortices.
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