Prog. Theor. Phys. Vol. 85 No. 3 (1991) pp. 509-525
Zeros of Partition Function and High Temperature Expansion for the Two-Dimensional Ising Models
Department of Pure and Applied Sciences, University of Tokyo, Tokyo 153,
*Department of Physics, University of Pennsylvania, Philadelphia, PA 19104
(Received November 8, 1990)
Distribution of zeros of partition function Z without magnetic field is studied for some two-dimensional Ising models with nearst-neighbor interactions. The distributions are presented graphically for the honeycomb, triangular diced and Kagomé lattices. It is shown that an asymptotic form of high temperature expansion for ln
Z is closely related with the distribution of zeros. The expansion coefficients are derived up to large orders by computer for the honeycomb and Kagomé lattices. It turns out that their oscillatory behaviors are understood very well by studying the zeros off the positive real axis, in particular the period of oscillation for the Kagomé lattice is proved to be about 5.25.
DOI : 10.1143/PTP.85.509
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