The microcanonical transfer matrix and its extensions offer a new way of obtaining exact partition functions on finite two dimensional lattices. We show the density of the partition function zeros in the complex x- plane for the Ising model at $y=y_c$ and $y=0.5y_c$ , and the density of the partition function zeros in the complex y-plane for the three-state Potts model.The microcanonical transfer matrix and its extensions offer a new way of obtaining exact partition functions on finite two dimensional lattices. We show the density of the partition function zeros in the complex x- plane for the Ising model at $y=y_c$ and $y=0.5y_c$, and the density of the partition function zeros in the complex y-plane for the three-state Potts model.

arXiv:cond-mat/9909390Sep 28, 19990 citations

Yang-Lee Zeros of the Q-State Potts Model in the Complex Magnetic Field Plane

Seung‐Yeon Kim, Richard J. Creswick

The microcanonical transfer matrix is used to study the distribution of Yang-Lee zeros of the $Q$ -state Potts model in the complex magnetic field ( ${x\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}e}^{\ensuremath{\beta}h}$) plane for the first time. Finite size scaling suggests that at (and below) the critical temperature the zeros lie close to, but not on, the unit circle with the two exceptions of the critical point $x\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ ( $h\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ ) itself and the zeros in the limit $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ .The microcanonical transfer matrix is used to study the distribution of Yang-Lee zeros of the $Q$-state Potts model in the complex magnetic field ( ${x\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}e}^{\ensuremath{\beta}h}$) plane for the first time. Finite size scaling suggests that at (and below) the critical temperature the zeros lie close to, but not on, the unit circle with the two exceptions of the critical point $x\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ ( $h\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$) itself and the zeros in the limit $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$.

arXiv:cond-mat/9807360Physical Review LettersSep 1, 199854 citations

Monte Carlo simulation for the quantum q-state Potts model

C. Y. Pan

Journal of Magnetism and Magnetic MaterialsFeb 1, 19920 citations

Yang-Lee Zeros of the One-Dimensional Q-State Potts Model

Seung-Yeon Kim

The distributions of the Yang-Lee zeros of the ferromagnetic and antiferromagnetic Q-state Potts models in one dimension are studied for arbitrary Q and temperature. The Yang-Lee zeros of the Potts antiferromagnet have been fully investigated for the first time. The distributions of the Yang-Lee zeros show a variety of different shapes. Some of the Yang-Lee zeros lie on the positive real axis even for T>0. For the ferromagnetic model this happens only for Q<1, while there exist some zeros of the antiferromagnetic model on the positive real axis both for Q<1 and for Q>1.The distributions of the Yang-Lee zeros of the ferromagnetic and antiferromagnetic Q-state Potts models in one dimension are studied for arbitrary Q and temperature. The Yang-Lee zeros of the Potts antiferromagnet have been fully investigated for the first time. The distributions of the Yang-Lee zeros show a variety of different shapes. Some of the Yang-Lee zeros lie on the positive real axis even for T>0. For the ferromagnetic model this happens only for Q<1, while there exist some zeros of the antiferromagnetic model on the positive real axis both for Q<1 and for Q>1.

arXiv:cond-mat/0305456Journal of the Korean Physical SocietyMar 15, 20044 citations

y=y_c

and

y=0.5y_c

, and the density of the partition function zeros in the complex y-plane for the three-state Potts model.

The microcanonical transfer matrix is used to study the distribution of Yang-Lee zeros of the

Q

-state Potts model in the complex magnetic field ( ${x\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}e}^{\ensuremath{\beta}h}$) plane for the first time. Finite size scaling suggests that at (and below) the critical temperature the zeros lie close to, but not on, the unit circle with the two exceptions of the critical point

x\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1

(

h\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0

) itself and the zeros in the limit

T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0