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

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Critical line of an anisotropic Ising antiferromagnet on square and honeycomb lattices

Xianzhi Wang, Jai Sam Kim

Published Sep 1, 1997• 15 citations
Publisher

Abstract

Using the approach that we developed recently, we find the critical line of an anisotropic Ising antiferromagnet on two-dimensional square and honeycomb lattices. We extend our previous lemma and conjecture to be useful in the antiferromagnetic system. We find two interesting behaviors: (1) An antiferromagnet is not necessarily most inert at the absolute zero. (2) The field-driven antiferromagnetic phase transition is possible in the honeycomb lattice.

DOI
10.1103/physreve.56.2793

Related papers

Critical line of honeycomb-lattice anisotropic Ising antiferromagnets in a field

S. L. A. de Queiroz

Numerical transfer-matrix methods are used to discuss the shape of the phase diagram, in field-temperature parameter space, of two-dimensional honeycomb-lattice Ising spin-1/2 magnets, with antiferromagnetic couplings along at least one lattice axis, in a uniform external field. Both the order and universality class of the underlying phase transition are examined as well. Our results indicate that in one particular case, the critical line has, at least to a very good approximation, a horizontal section (i.e., at constant field) of finite length, starting at the zero-temperature end of the phase boundary. Other than that, we find no evidence of unusual behavior, at variance with the re-entrant features predicted in earlier studies.

arXiv:1210.1437•Physical Review E•Feb 13, 2013•2 citations

The Critical Line of an Ising Antiferromagnet on Square and Honeycomb Lattices

Xianzhi Wang, Jai Sam Kim

We show that the singularity of the free energy of Ising models in the absence of a magnetic field on the triangular, square, and honeycomb lattices is related to zeros of the pseudopartition function on an elementary cycle. Using the Griffiths' smoothness postulate, we extend these results to the case in a magnetic field and derive a formula of the critical line of an Ising antiferromagnet, which is in good agreement with the numerical results.

Physical Review Letters•Jan 20, 1997•44 citations

The Critical Lines of the Yang–Lee Edge Singularities of the Anisotropic Ising Ferromagnets on Square, Triangular and Honeycomb Lattices

Xianzhi Wang

Using the numerical results and some results from the renormalization group theory, we extend our previous approach of determining the Yang–Lee edge singularities of Ising ferromagnets on square, triangular and honeycomb lattices (Phys. Rev. Lett. 78 (1997) 413; Phys. Rev. E56 (1998) 2793; E57 (1998) 5013) and obtain accurate closed-form approximations of the critical lines of anisotropic Ising ferromagnets on these lattices.

Communications in Theoretical Physics•Mar 15, 2001•2 citations

The Critical Lines of the Yang—Lee Edge Singularities of the Anisotropic Ising Ferromagnets on Square,Triangular and Honeycomb Lattices

WANGXian-Zhi

Using the numerical results and some results from the renormalization group theory, we extend our previous approach of determining the Yang-Lee edge singularities of Ising ferromagnets on square, triangular and honeycomb lattices (Phys. Rev. Lett. 78 (1997) 413; Phys. Rev. E56 (1998) 2793; E57 (1998) 5013) and obtain accurate closed-form approximations of the critical lines of anisotropic Ising ferromagnets on these lattices.

理论物理通讯：英文版•Jan 1, 2001•0 citations

Ising antiferromagnets on honeycomb and square lattices in the critical magnetic field

Seung‐Yeon Kim

The important properties of the Ising antiferromagnets on honeycomb lattice and square lattice in the critical magnetic field B c (B c = 3|J| for honeycomb lattice and B c = 4|J| for square lattice with coupling constant J) are investigated by evaluating exactly all their possible ground states on L × 2L honeycomb lattices (L = 4 ∼ 14) and L × L square lattices (L = 4 ∼ 16) with cylindrical boundary conditions. In particular, the properties of the honeycomb-lattice Ising antiferromagnet in the critical magnetic field B c are unveiled for the first time.

Journal of the Korean Physical Society•Dec 1, 2012•2 citations

Critical lines of the Yang-Lee edge singularity of Ising ferromagnets on square, triangular, and honeycomb lattices

Xianzhi Wang, Jai Sam Kim

We extend our previous approach to determine the critical lines of the Yang-Lee edge singularity of Ising ferromagnets on square, triangular, and honeycomb lattices by considering the zeros of the Ising partition function on elementary cycles of these lattices. It is found that the critical lines have the properties ${h}_{0}\ensuremath{\rightarrow}{t}^{15/8}$ as $\stackrel{\ensuremath{\rightarrow}}{T}{T}_{c}+$ and $\ensuremath{\beta}{h}_{0}\ensuremath{\rightarrow}\ensuremath{\pi}/2$ as $\stackrel{\ensuremath{\rightarrow}}{T}\ensuremath{\infty}$. Using the asymptotic formulas valid in the high-temperature limit and the zero-field limit we obtain the functional form of the critical line.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•May 1, 1998•10 citations
Using the approach that we developed recently, we find the critical line of an anisotropic Ising antiferromagnet on two-dimensional square and honeycomb lattices. We extend our previous lemma and conjecture to be useful in the antiferromagnetic system. We find two interesting behaviors: (1) An antiferromagnet is not necessarily most inert at the absolute zero. (2) The field-driven antiferromagnetic phase transition is possible in the honeycomb lattice.
Numerical transfer-matrix methods are used to discuss the shape of the phase diagram, in field-temperature parameter space, of two-dimensional honeycomb-lattice Ising spin-1/2 magnets, with antiferromagnetic couplings along at least one lattice axis, in a uniform external field. Both the order and universality class of the underlying phase transition are examined as well. Our results indicate that in one particular case, the critical line has, at least to a very good approximation, a horizontal section (i.e., at constant field) of finite length, starting at the zero-temperature end of the phase boundary. Other than that, we find no evidence of unusual behavior, at variance with the re-entrant features predicted in earlier studies.
The important properties of the Ising antiferromagnets on honeycomb lattice and square lattice in the critical magnetic field B c (B c = 3|J| for honeycomb lattice and B c = 4|J| for square lattice with coupling constant J) are investigated by evaluating exactly all their possible ground states on L × 2L honeycomb lattices (L = 4 ∼ 14) and L × L square lattices (L = 4 ∼ 16) with cylindrical boundary conditions. In particular, the properties of the honeycomb-lattice Ising antiferromagnet in the critical magnetic field B c are unveiled for the first time.
We extend our previous approach to determine the critical lines of the Yang-Lee edge singularity of Ising ferromagnets on square, triangular, and honeycomb lattices by considering the zeros of the Ising partition function on elementary cycles of these lattices. It is found that the critical lines have the properties ${h}_{0}\ensuremath{\rightarrow}{t}^{15/8}$ as $\stackrel{\ensuremath{\rightarrow}}{T}{T}_{c}+$ and $\ensuremath{\beta}{h}_{0}\ensuremath{\rightarrow}\ensuremath{\pi}/2$ as $\stackrel{\ensuremath{\rightarrow}}{T}\ensuremath{\infty}$. Using the asymptotic formulas valid in the high-temperature limit and the zero-field limit we obtain the functional form of the critical line.