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 ($H_{\mathrm{sp})}$ 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 $H_{\mathrm{sp}}$ from the exact Hamiltonian.