Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Why spin ice obeys the ice rules   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.

22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
2
The categories of this paper are: math
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph