Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Chinese Physics Letters

Yang-Lee Circle Theorem for an Antiferromagnetic Heisenberg Ladder

Xianzhi Wang

Published Jul 1, 2001• 2 citations
Publisher

Abstract

The Yang-Lee zeros of an antiferromagnetic Heisenberg ladder model are determined. It is found that if J4≤0 Yang-Lee zeros are located on the unit circle and on the negative real axis in the complex activity plane. In particular, if J4≤0 and 2J2≥J4, Yang-Lee zeros are located on the unit circle and the Yang-Lee circle theorem is valid. If J4>0, Yang-Lee zeros are located on some complicated curves.

DOI
10.1088/0256-307x/18/7/336

Related papers

Lee-Yang Theorem and the Griffiths Inequality for the Anisotropic Heisenberg Ferromagnet

Taro Asano

It is shown that the zeros of the partition function of the anisotropic Heisenberg ferromagnet locate on the unit circle in the complex "fugacity" plane, and all the spin correlation functions are non-negative when no external magnetic field is present.

Physical Review Letters•Jun 22, 1970•56 citations

Yang-Lee Zeros of the Antiferromagnetic Ising Model

Seung‐Yeon Kim

There exists the famous circle theorem on the Yang-Lee zeros of the ferromagnetic Ising model. However, the Yang-Lee zeros of the antiferromagnetic Ising model are much less well understood than those of the ferromagnetic model. The precise distribution of the Yang-Lee zeros of the antiferromagnetic Ising model only with nearest-neighbor interaction J on LxL square lattices is determined as a function of temperature a=e(2betaJ) (J<0), and its relation to the phase transitions is investigated. In the thermodynamic limit (L-->infinity), the distribution of the Yang-Lee zeros of the antiferromagnetic Ising model cuts the positive real axis in the complex x=e(-2betaH) plane, resulting in the critical magnetic field +/-H(c)(a), where H(c)>0 below the critical temperature a(c)=square root of 2-1. The results suggest that the value of the scaling exponent y(h) is 1 along the critical line for a<a(c).

Physical Review Letters•Sep 23, 2004•68 citations

Yang-Lee circle theorem for an ideal pseudospin-1/2 Bose gas in an external magnetic field

Xian Zhi Wang

The Yang-Lee circle theorem is extended to an ideal pseudospin-1/2 Bose gas in an external magnetic field. It is found that the zeros of the canonical partition function are located on the unit circle in the complex activity plane if the temperature is above the critical temperature of ideal Bose-Einstein condensation. No zeros exist if the temperature is below the critical temperature.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Mar 21, 2001•8 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.

arXiv:1508.07751•Physical Review B•Sep 17, 2015•15 citations

Yang-Lee zeros of one-dimensional quantum many-body systems

Xianzhi Wang, Jai Sam Kim

We obtain a generic formula for the distribution of Yang-Lee zeros of one-dimensional quantum many-body systems solvable by the Bethe ansatz and the Yang-Yang thermodynamic formalism. We find that the zeros are located on the negative real axis of the complex fugacity plane and thus prove that no phase transition occurs in these one-dimensional systems, as proved by others using different methods.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Jan 1, 1999•4 citations

Generalized Lee-Yang's Theorem

Taro Asano

Lee-Yang's theorem which states that all the roots of the partition function of the ferromagnetic Ising model of spin 1/2 lie on the unit circle in the complex `fugacity' plane is generalized to the case of S =1 and 3/2, where S is the magnitude of the spin.

Journal of the Physical Society of Japan•Nov 1, 1968•19 citations
The Yang-Lee zeros of an antiferromagnetic Heisenberg ladder model are determined. It is found that if J4≤0 Yang-Lee zeros are located on the unit circle and on the negative real axis in the complex activity plane. In particular, if J4≤0 and 2J2≥J4, Yang-Lee zeros are located on the unit circle and the Yang-Lee circle theorem is valid. If J4>0, Yang-Lee zeros are located on some complicated curves.
There exists the famous circle theorem on the Yang-Lee zeros of the ferromagnetic Ising model. However, the Yang-Lee zeros of the antiferromagnetic Ising model are much less well understood than those of the ferromagnetic model. The precise distribution of the Yang-Lee zeros of the antiferromagnetic Ising model only with nearest-neighbor interaction J on LxL square lattices is determined as a function of temperature a=e(2betaJ) (J<0), and its relation to the phase transitions is investigated. In the thermodynamic limit (L-->infinity), the distribution of the Yang-Lee zeros of the antiferromagnetic Ising model cuts the positive real axis in the complex x=e(-2betaH) plane, resulting in the critical magnetic field +/-H(c)(a), where H(c)>0 below the critical temperature a(c)=square root of 2-1. The results suggest that the value of the scaling exponent y(h) is 1 along the critical line for a<a(c).
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 qqq-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>2q>2q>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)(q=3,4,5,6)(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.