  Recent experiments on the spin-ice material Dy2Ti2O7 suggest that the Pauling
"ice entropy", characteristic of its classical Coulombic spin-liquid state, may
be lost at low temperatures [D. Pomaranski et al., Nature Phys. 9, 353 (2013)].
However, despite nearly two decades of intensive study, the nature of the
equilibrium ground state of spin ice remains uncertain. Here we explore how
long-range dipolar interactions D, short-range exchange interactions, and
quantum fluctuations combine to determine the ground state of dipolar spin ice.
We identify a new organisational principle, namely that ordered ground states
are selected from a set of "chain states" in which dipolar interactions are
exponentially screened. Using both quantum and classical Monte Carlo
simulation, we establish phase diagrams as a function of quantum tunneling g,
and temperature T, and find that only a very small g_c << D is needed to
stabilize a quantum spin-liquid ground state. We discuss the implications of
these results for Dy2Ti2O7.
