Exact Solution of the $F$ Model of An Antiferroelectric

The Rys $F$ model of an antiferroelectric is solved by the transfer-matrix method. The result is different in many respects from the analogous Ising antiferromagnet, i.e., an infinite-order phase transition and a natural boundary in the complex $T$ plane. It can also be solved when an external electric field is included. Above the transition temperature the behavior is normal while below $T_c$ there is no polarization unless the electric field is sufficiently large.