Exactly Soluble Model of the Ferroelectric Phase Transition in Two Dimensions

The Slater model of the two-dimensional potassium dihydrogen phosphate crystal is solved exactly under the additional assumption that the dipoles are excluded from pointing along one direction of the crystal axis. The Curie temperature ${T}_{c}$ is not affected by this additional assumption but the phase change becomes a second-order transition. Complete polarization occurs below ${T}_{c}$ with specific heat $\ensuremath{\sim}{(T\ensuremath{-}{T}_{c})}^{\ensuremath{-}\frac{1}{2}}$ near and above the Curie point.