  While particle-based ices are often considered essentially equivalent to
magnet-based spin ices, the two differ essentially in frustration and
energetics. We show that at equilibrium particle-based ices correspond exactly
to spin ices coupled to a background field. In trivial geometries, such a field
has no effect, and the two systems are indeed thermodynamically equivalent. In
other cases, however, the field controls a richer phenomenology, absent in
magnetic ices, and still largely unexplored: ice rule fragility, topological
charge transfer, radial polarization, decimation induced disorder, and
glassiness.
