  Disorder in materials may be used to tune their functionalities, but much
more strikingly, its presence can entail entirely new behavior. This happens in
charge-ice where structural disorder is not weak and local, but strong and
long-range correlated. Here, two cations of different charge occupy a
pyrochlore lattice, arranging themselves such that all tetrahedra host two
cations of each type. The ensuing correlated disorder is characterized by
randomly packed loops of a single cation-type. If the cations are magnetic and
interact antiferromagnetically, a new type of magnet with strong interactions
along the loops, but frustrated interactions between loops, emerges. This
results in an ensemble of intertwined Heisenberg spin chains that form an
algebraic spin liquid at intermediate temperatures. At lower temperatures, we
find these non-local degrees of freedom undergo a discontinuous transition to a
spin nematic. While this phase does not break time reversal symmetry, its spin
symmetry is reduced resulting in a dramatically slower spin relaxation. The
transition is sensitive to the statistics of the cation loops, providing both a
direct thermodynamic signature of otherwise elusive structural information and
a structural route to engineering nematic phase stability.
