  We present a combined analytical and numerical study of the entropy as a
function of magnetization for an orientable 2D spin-ice model that exhibits a
Kasteleyn transition. The model that we use is related to the well known
six-vertex model but, as we show, our representation of it is more convenient
for constructing approximate expressions for the entropy at fixed
magnetization. We also discuss directions for further work, including the
possibility of deforming our model into one exhibiting a quantum Kasteleyn
transition.
