Distribution of Zeros of the Partition Function for the Slater Model of Ferroelectricity

Abstract

The partition functions of the Slater's models of ferroelectricity (KDP model), antiferroelectricity (F model) and Wu's modified KDP model are calculated for lattices of finite size (up to 6×6). The distributions of the zeros of the partition function of the KDP model in the complex fugacity ( z ≡exp V / k T ) plane are on the unit circle at low temperatures and are two-dimensionally distributed at high temperatures. In case of the F model the distribution of zeros are two-dimensional in all temperature region. The zeros of the KDP model at low temperatures in the complex z 2 N plane are on the unit circle, and those at high temperatures lie on the negative real axis. The zeros of the F model in the complex z 2 N plane lie on the negative real axis at high and low temperatures. The distribution of zeros of the KDP model, the F model and the modified KDP model in the complex temperature plane are also obtained.