Dipolar spin correlations in classical pyrochlore magnets

A theory of the T→ 0 spin correlations of nearest-neighbor O(N) magnets on the pyrochlore lattice when they are paramagnetic down to T=0 was formulated. The classical nearest-neighbor antiferromagnet on the pyrochlore lattice was also considered. It was observed that a local constraint obeyed by the extensively degenerate ground states dictated a dipolar form for the asymptotic spin correlations. It was found that a simple analytical expression for the correlations of the equivalent models of spin ice and cubic water ice was also obtained.