Dimer models for the antiferroelectric transition in copper formate tetrahydrate

This paper develops the lattice statistical theory of the antiferroelectric transition in copper formate tetrahydrate in terms of dimer and 8-vertex models. The simplest dimer model is shown to be inappropriate for describing the transition, primarily because the hydrogens order into the wrong ground-state configuration. In the context of the dimer model, we introduce two exactly solvable modifications by postulating additional, physically plausible short-range interactions in the hydrogen bonding. The first model, which results from asymmetrically weighting the dimer positions, does have the observed ``frozen'' ground state and residual short-range order above Tc, but the transition is continuous. The second model introduces repulsive interactions between nearest-neighbor parallel dimer positions via the Baxter formulation of the dimer model in terms of the 8-vertex model. A suitable lattice transformation enables us to develop the model in terms of a generalized KDP model. This model has a first-order transition with a maximum allowable transition entropy of 0.876 cal/deg · mole, in excellent agreement with that determined from specific heat measurements. The higher energy hydrogen configurations are of the order of kT, indicative of the nature of the thermal excitations.