  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 completely degeneracy 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.
