Why spin ice obeys the ice rules

TL;DR

This paper explains why spin ice materials follow the ice rules despite long-range dipole interactions, by constructing a simplified model with equivalent ground states and introducing the concept of projective equivalence.

Contribution

The authors demonstrate that a tailored short-range dipole interaction model reproduces the ground states of the true long-range interactions, revealing a new concept of projective equivalence.

Findings

Model dipole interaction matches ground states of true dipole interactions.

Small differences between models reproduce numerical results.

Introduces the concept of projective equivalence between interactions.

Abstract

The low temperature entropy of the the spin ice compounds, such as Ho$_2$Ti$_2$O$_7$ and Dy$_2$Ti$_2$O$_7$, 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.