  Certain classical statistical systems with strong local constraints are known
to exhibit Coulomb phases, where long-range correlation functions have
power-law forms. Continuous transitions from these into ordered phases cannot
be described by a naive application of the Landau-Ginzburg-Wilson theory, since
neither phase is thermally disordered. We present an alternative approach to a
critical theory for such systems, based on a mapping to a quantum problem in
one fewer spatial dimensions. We apply this method to spin ice, a magnetic
material with geometrical frustration, which exhibits a Coulomb phase and a
continuous transition to an ordered state in the presence of a magnetic field
applied in the [100] direction.
