  Dy2Ti2O7 is a geometrically frustrated magnetic material with a strongly
correlated spin ice regime that extends from 1 K down to as low as 60 mK. The
diffuse elastic neutron scattering intensities in the spin ice regime can be
remarkably well described by a phenomenological model of weakly interacting
hexagonal spin clusters, as invoked in other geometrically frustrated magnets.
We present a highly refined microscopic theory of Dy2Ti2O7 that includes
long-range dipolar and exchange interactions to third nearest neighbors and
which demonstrates that the clusters are purely fictitious in this material.
The seeming emergence of composite spin clusters and their associated
scattering pattern is instead an indicator of fine-tuning of ancillary
correlations within a strongly correlated state.
