Heat capacity measurements recently showed that CO physisorbed on grap
hite undergoes a head-tail ordering transition at roughly 5 K. The pre
sent paper is a detailed Monte Carlo study of this phase transition an
d the ordered state, The simulations are based on an ab initio pair po
tential and rely crucially on a thorough finite-size scaling study of
various quantities. In agreement with experiments we find that the tra
nsition belongs to the universality class of the Ising model in two di
mensions. We go beyond experimental knowledge by revealing the particu
lar ferrielectric structure of the ground state, and show that the tra
nsition is due to the molecule's shape asymmetry rather than to electr
ostatic dipole interactions. The influence of quantum fluctuations on
the ground state and on the transition itself are also analyzed.