Monte Carlo studies of the dipolar spin ice model

We present a detailed overview of numerical Monte Carlo studies of the dipolar spin ice model, which has been shown to be an excellent quantitative descriptor of the Ising pyrochlore materials Dy 2 Ti 2 O 7 and Ho 2 Ti 2 O 7 . We show that the dipolar spin ice model can reproduce an effective quasi -macroscopically degenerate ground state and spin ice behaviour of these materials when the long range nature of dipole–dipole interaction is handled carefully using Ewald summation techniques. This degeneracy is, however, ultimately lifted at low temperature. The long range ordered state is identified via Monte Carlo simulation techniques. Finally, we investigate the behaviour of the dipolar spin ice model in an applied magnetic field and compare our predictions to experimental results. We find that a number of different long range ordered ground states are favoured by the model, depending on field direction.