  We examine the statistical mechanics of spin-ice materials with a [100]
magnetic field. We show that the approach to saturated magnetisation is, in the
low-temperature limit, an example of a 3D Kasteleyn transition, which is
topological in the sense that magnetisation is changed only by excitations that
span the entire system. We study the transition analytically and using a Monte
Carlo cluster algorithm, and compare our results with recent data from
experiments on Dy2Ti2O7.
