Orientational Phases of Hydrogen Molecules on a Triangular Lattice

A mean-field theory for the ordering of hydrogen molecules on a triangular net is derived in terms of the quadrupole coupling constant Γ, the crystal field Vc, and the temperature T. The phase diagram consists of six regions, separated by first- and second-order transitions. For almost all values of VcΓ for which ordering occurs, the disordered to ordered phase transition is continuous. At $T=0$ K, all phases have energy gaps except for a ferrorotational phase which behaves like an XY model.