Ordering of Ising dipoles

The ordering properties of Ising dipoles are studied in mean field theory, and by Monte Carlo simulations. The boundary conditions are such that there is no net depolarizing field and both regular lattices and various random arrangements are considered. In the mean field approach the authors employ the replica method with a Gaussian approximation for the distribution of dipole-dipole interactions, while a Kirkwood approximation is used for the spatial distribution of dipoles. The low-temperature phase for a system of randomly parked dipoles and diluted face centred cubic and body centred cubic lattices is found to be ferro-electric above a critical concentration. Below this concentration the mean field theory predicts a spin glass. The simulations are only carried out for the body centred cubic lattice. The transition temperature to the ferroelectric state is determined from finite size scaling of the mean square polarization. The critical concentration for the occurrence of a spin glass phase is estimated by zero temperature Monte Carlo simulations using the simulated annealing method. The results are found to be in qualitative agreement with those of the mean field theory described above.