The effects of quantum fluctuations on the ''2-in'' herringbone orderi
ng in a realistic model of 900 N2 molecules adsorbed in the (square-ro
ot 3 x square-root 3)R30-degrees structure on graphite are studied via
path-integral Monte Carlo (PIMC) simulations. Quasiclassical and quas
iharmonic calculations agree for high and low temperatures, respective
ly, but only PIMC gives satisfactory results over the entire temperatu
re range. We can quantify the lowering of the transition temperature a
nd the depression of the ground state order to 10% as compared to clas
sical modeling.