The low temperature entropy of the the spin ice compounds, such as Ho2Ti2O7 and Dy2Ti2O7, is well described by the nearest-neighbor antiferromagnetic Ising model on the pyrochlore lattice, i.e.\ by the ``ice rules''. This is surprising since the dominant coupling between the spins is their long ranged dipole interaction. We show that this phenomenon can be understood rather elegantly: one can construct a model dipole interaction, by adding terms of shorter range, which yields {\it precisely} the same ground states, and hence T=0 entropy, as the nearest neighbor interaction. A treatment of the small difference between the model and true dipole interactions reproduces the numerical work by Gingras et al in detail. We are also led to a more general concept of projective equivalence between interactions.
@article{arxiv.cond-mat/0502137,
title = {Why spin ice obeys the ice rules},
author = {S. V. Isakov and R. Moessner and S. L. Sondhi},
journal= {arXiv preprint arXiv:cond-mat/0502137},
year = {2007}
}