Classical to 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 naïve 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.