Classical-Quantum Mappings for Geometrically Frustrated Systems: Spin Ice in a [100] Field

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.