Power-law spin correlations in pyrochlore antiferromagnets

The ground state ensemble of the highly frustrated pyrochlore-lattice antiferromagnet can be mapped to a coarse-grained ``polarization'' field satisfying a zero-divergence condition From this it follows that the correlations of this field, as well as the actual spin correlations, decay with separation like a dipole-dipole interaction ($1/|R|^3$). Furthermore, a lattice version of the derivation gives an approximate formula for spin correlations, with several features that agree well with simulations and neutron-diffraction measurements of diffuse scattering, in particular the pinch-point (pseudo-dipolar) singularities at reciprocal lattice vectors. This system is compared to others in which constraints also imply diffraction singularities, and other possible applications of the coarse-grained polarization are discussed.