Exact Solution of a Two-Dimensional Model for Hydrogen-Bonded Crystals

A model of two-dimensional hydrogen-bonded crystals satisfying the ice rule is presented and solved exactly in the presence of an external electric field. The transfer-matrix method is used. The model includes, for special values of the parameters, the ice problem, the Rys $F$ model of an antiferroelectric, and the Slater KDP model of a ferroelectric.