A mean field theory is developed which is applicable to the orientational behavior of (J = 1) hydrogen molecules on the surface of Grafoil. The hydrogen molecules are assumed to form a triangular lattice in a weak, axially symmetric crystal field, Vc. perpendicular to the substrate and to interact via the electric quadrupole–quadrupole interaction with nearest-neighbor coupling constant Γ. Free energy calculations for the various possible ordered phases are presented, and a Landau expansion is used to investigate the phase boundary between the disordered and ordered phases. A computer calculation, based on the iterative method of James, is used to determine the lines of transition between ordered phases. For almost all values of Vc < 22.5Γ, the disordered to ordered state phase transition is continuous. Four distinct types of ordered phases are found — a four-sublattice phase, two two-sublattice phases, and a one-sublattice phase which resembles an X–Y model. Comparison is made to the recent nmr data of Kubik and Hardy for H2 and D2 on Grafoil.
A quantum simulation approach for a three-dimensional Ising spin model—Comparison to mean field theory
