We study phase transitions in classical spin ice at nonzero magnetization, by introducing a mean-field theory designed to capture the interplay between confinement and topological constraints. The method is applied to a model of spin ice in an applied magnetic field along the [1 0 0] crystallographic direction and yields a phase diagram containing the Coulomb phase as well as a set of magnetization plateaux. We argue that the lobe structure of the phase diagram, strongly reminiscent of the Bose–Hubbard model, is generic to Coulomb spin liquids.
Powell, S. (2017). Mean-field theory for confinement transitions and magnetization plateaux in spin ice. Journal of Physics A: Mathematical and Theoretical, 50(12), https://doi.org/10.1088/1751-8121/aa5bc6