Exact Solution of a Model of an Antiferroelectric Transition

A modified version of the Rys $F$ model of an antiferroelectric is solved exactly. In addition to the six kinds of vertices allowed by the ice rule, the model considered also includes two kinds of doubly ionized vertices. For a particular choice of the energy for these new vertices, the partition function is evaluated in a closed form. The phase transition is of second-order (in contradistinction to the infinite-order transition of the Rys $F$ model), and the specific heat has a logarithmic singularity.