Lennard-Jones molecules on a two-dimensional lattice: A model anisotropic XY system

We explore different procedures for obtaining effective spin Hamiltonians of anisotropic XY form (Hsp) for diatomic molecules whose centers of mass and molecular axis orientations are confined to a two-dimensional plane and which interact via atom-atom Lennard-Jones potentials. By comparing spin-wave, molecular-field, and Monte Carlo studies of the resulting spin Hamiltonians with molecular-dynamics simulation of the actual system, we evaluate the adequacy of these procedures to obtain Hsp from the exact Hamiltonian. © 1985 The American Physical Society.