The modified potassium dihydrogen phosphate (KDP) model of a two-dimensional ferroelectric with the inclusion of an arbitrary electric field $\mathcal{E}$ is considered. The nature of the phase transition is unaffected by the inclusion of an external field, whereas the transition temperature depends on $\mathcal{E}$ with $T_c\to \infty$ as $\mathcal{E}\to \infty$, and $T_c\to 0$ as $\mathcal{E}\to \mathrm{some}\mathrm{special}\mathrm{values}$. We also find that $T_c$ is determined by different relations in different regions in the $\mathcal{E}$ plane, a property not shared by the Slater KDP model. Among the other thermodynamic properties discussed, the critical behavior of the polarizability is shown to be $\chi \sim {(T-T_c)}^{-\frac{1}{2}}$. It is shown that this model is identical to the problem of close-packed dimers on a hexagonal lattice.

• Received 4 December 1967

DOI:https://doi.org/10.1103/PhysRev.168.539