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The phase diagram of the classical \jj model on the \kag lattice isinvestigated using extensive \mc simulations. In a realistic range ofparameters, this model has a low-temperature chiral-ordered phase withoutlong-range spin order. We show that the critical transition marking thedestruction of chiral order is preempted by the first order proliferation of\Zdeux point defects. The core energy of these vortices appears to vanish whenapproaching the T=0 phase boundary, where both \Zdeux defects and gaplessmagnons contribute to disordering the system at very low temperature. Thissituation might be typical of a large class of frustrated magnets. Possiblerelevance for real materials is also discussed.

Chirality and $Z_2$ vortices in an Heisenberg spin model on the kagom\'e lattice