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

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 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

Density of Yang-Lee zeros in the thermodynamic limit from tensor network methods

Artur García-Sáez, Tzu-Chieh Wei

The distribution of Yang-Lee zeros in the ferromagnetic Ising model in both two and three dimensions is studied on the complex field plane directly in the thermodynamic limit via the tensor network methods. The partition function is represented as a contraction of a tensor network and is efficiently evaluated with an iterative tensor renormalization scheme. The free-energy density and the magnetization are computed on the complex field plane. Via the discontinuity of the magnetization, the density of the Yang-Lee zeros is obtained to lie on the unit circle, consistent with the Lee-Yang circle theorem. Distinct features are observed at different temperatures---below, above, and at the critical temperature. Application of the tensor network approach is also made to the $q$ -state Potts models in both two and three dimensions and a previous debate on whether, in the thermodynamic limit, the Yang-Lee zeros lie on a unit circle for $q>2$ is resolved: they clearly do not lie on a unit circle except at the zero temperature. For the Potts models $(q=3,4,5,6)$ investigated in two dimensions, as the temperature is lowered the radius of the zeros at a fixed angle from the real axis shrinks exponentially towards unity with the inverse temperature.The distribution of Yang-Lee zeros in the ferromagnetic Ising model in both two and three dimensions is studied on the complex field plane directly in the thermodynamic limit via the tensor network methods. The partition function is represented as a contraction of a tensor network and is efficiently evaluated with an iterative tensor renormalization scheme. The free-energy density and the magnetization are computed on the complex field plane. Via the discontinuity of the magnetization, the density of the Yang-Lee zeros is obtained to lie on the unit circle, consistent with the Lee-Yang circle theorem. Distinct features are observed at different temperatures---below, above, and at the critical temperature. Application of the tensor network approach is also made to the $q$-state Potts models in both two and three dimensions and a previous debate on whether, in the thermodynamic limit, the Yang-Lee zeros lie on a unit circle for $q>2$ is resolved: they clearly do not lie on a unit circle except at the zero temperature. For the Potts models $(q=3,4,5,6)$ investigated in two dimensions, as the temperature is lowered the radius of the zeros at a fixed angle from the real axis shrinks exponentially towards unity with the inverse temperature.

arXiv:1508.07751Physical Review BSep 17, 201515 citations

Microcanonical transfer matrix study of the Q-state Potts model

Richard J. Creswick, Seung‐Yeon Kim

arXiv:cond-mat/9810153Computer Physics CommunicationsSep 1, 199911 citations

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

q

-state Potts models in both two and three dimensions and a previous debate on whether, in the thermodynamic limit, the Yang-Lee zeros lie on a unit circle for

q>2

is resolved: they clearly do not lie on a unit circle except at the zero temperature. For the Potts models

(q=3,4,5,6)

investigated in two dimensions, as the temperature is lowered the radius of the zeros at a fixed angle from the real axis shrinks exponentially towards unity with the inverse temperature.