Circle Theorem for the Ice-Rule Ferroelectric Models

We show that the circle theorem on the distribution of zeros of the partition function breaks down for the ferroelectric potassium dihydrogen phosphate (KDP) model if the field lies outside the first quadrant. We also use a recent result by Suzuki and Fisher to establish the circle theorem for the antiferroelectric $F$ model with a staggered electric field. Numerical results on the distribution of zeros for a 4 × 4 lattice are given.