We study spin correlations for the highly frustrated classical pyrochlore lattice antiferromagnets with O(N) symmetry in the limit T->0. We conjecture that a local constraint obeyed by the extensively degenerate ground states dictates a dipolar form for the asymptotic spin correlations, at all N = 2 for which the system is paramagnetic down to T=0. We verify this conjecture in the cases N=1 and N=3 by simulations and to all orders in the 1/N expansion about the solvable N=infinity limit. Remarkably, the N=infinity formulae are an excellent fit, at all distances, to the correlators at N=3 and even at N=1. Thus we obtain a simple analytical expression also for the correlations of the equivalent models of spin ice and cubic water ice, I_h.
@article{arxiv.cond-mat/0407004,
title = {Dipolar spin correlations in classical pyrochlore magnets},
author = {S. V. Isakov and K. Gregor and R. Moessner and S. L. Sondhi},
journal= {arXiv preprint arXiv:cond-mat/0407004},
year = {2016}
}