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

The phase diagram of the classical \jj model on the \kag lattice is investigated using extensive \mc simulations. In a realistic range of parameters, this model has a low-temperature chiral-ordered phase without long-range spin order. We show that the critical transition marking the destruction of chiral order is preempted by the first order proliferation of \Zdeux point defects. The core energy of these vortices appears to vanish when approaching the T=0 phase boundary, where both \Zdeux defects and gapless magnons contribute to disordering the system at very low temperature. This situation might be typical of a large class of frustrated magnets. Possible relevance for real materials is also discussed.