The orientational ordering of molecular hydrogen in 2D

The orientational ordering of ortho-hydrogen molecules on a triangular latt ice is calculated as a function of ortho concentration using the method of restricted traces. The calculated temperatures for the transitions from the disordered phase to the long range pinwheel ordered phase show a strong co ncentration dependence with a critical concentration X-c = 73% below which the long range ordering is not realized in this model. The results are cons istent with recent NMR studies of ortho-para hydrogen mixtures adsorbed as ;a commensurate root 3 x root 3 structure on hexagonal boron nitride for wh ich X-c = 69 +/- 4%. The values of the observed transition temperatures can only be understood if there is a large renormalization of the effective qu adrupolar interaction constant in 2D.