Distribution of Zeros of the Partition Function for the Slater Model of Ferroelectricity
Shigetoshi Katsura, Yoshihiko Abe, Katsuji Ohkohchi · Journal of the Physical Society of Japan · 1970
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.