  We study the anti-ferromagnetic six-state clock model with nearest neighbor
interactions on a triangular lattice with extensive Monte-Carlo simulations. We
find clear indications of two phase transitions at two different temperatures:
Below $T_I$ a chirality order sets in and by a thorough finite size scaling
analysis of the specific heat and the chirality correlation length we show that
this transition is in the Ising universality class (with a non-vanishing
chirality order parameter below $T_I$). At $T_{KT}(<T_I)$ the spin-spin
correlation length as well as the spin susceptibility diverges according to a
Kosterlitz-Thouless (KT) form and spin correlations decay algebraically below
$T_{KT}$. We compare our results to recent x-ray diffraction experiments on the
orientational ordering of CF$_3$Br monolayers physisorbed on graphite. We argue
that the six-state clock model describes the universal feature of the phase
transition in the experimental system and that the orientational ordering
belongs to the KT universality class.
