Long-Range Order at Low Temperatures in Dipolar Spin Ice

It has recently been suggested that long-range magnetic dipolar interactions are responsible for spin ice behavior in the Ising pyrochlore magnets Dy₂Ti₂O₇ and Ho₂Ti₂O₇. We report here numerical results on the low temperature properties of the dipolar spin ice model, obtained via a new loop algorithm which greatly improves the dynamics at low temperature. We recover the previously reported missing entropy in this model, and find a first order transition to a long-range ordered phase with zero total magnetization at very low temperature. We discuss the relevance of these results to Dy₂Ti₂O₇ and Ho₂Ti₂O₇.