A unified model for hydrogen bonded crystals

In this paper we propose a unified model for hydrogen-bonded crystals which includes proton hopping, interactions between protons and PO43− tetrahedra, and between PO43− tetrahedra. The protons are assumed to have two equilibrium states on the bonds and the states of the tetrahedra are modeled as s-dimensional unit vectors or (discrete) rotators. A decimation procedure over proton states is used to show that the model is equivalent to an order-disorder model for PO43− tetrahedra but with temperature-dependent interactions. Exact results are obtained for the case of two spatial and two rotator dimensions. Depending on the physical interpretation of the rotator states one obtains crossover from antiferroelectric to ferroelectric phases and vice versa, as well as isotope effects and a complete absence transition as the proton tunneling parameter is varied