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. B, Condensed matter

Ferrimagnetism in a one-dimensional Heisenberg model

Guang-Shan Tian

Published Sep 1, 1997• 43 citations
Publisher

Abstract

In this paper, we show that for a one-dimensional antiferromagnetic Heisenberg model with unequal spins, its absolute ground state has both antiferromagnetic and ferromagnetic long-range orders.Received 24 October 1996DOI:https://doi.org/10.1103/PhysRevB.56.5355©1997 American Physical Society

DOI
10.1103/physrevb.56.5355

Related papers

Antiferromagnetic order in the periodic Anderson model at half filling: A rigorous result

Guang-Shan Tian

By using a recent result of Ueda et al. [Phys. Rev. Lett 68, 1030 (1992)], we prove rigorously that the ground state of the symmetric periodic Anderson model has short-range antiferromagnetic order.Received 26 April 1994DOI:https://doi.org/10.1103/PhysRevB.50.6246©1994 American Physical Society

Physical review. B, Condensed matter•Sep 1, 1994•24 citations

Coexistence of the ferromagnetic and antiferromagnetic long-range orders in the generalized antiferromagnetic Heisenberg model on a bipartite lattice

Guang-Shan Tian

The concept of ferrimagnetism was first proposed by Neel to explain why some materials have a macroscopic magnetization but no ferromagnetic long-range order, when the temperature T is lower than a phase transition temperature T c . In this article, based on a theorem of Lieb and Mattis, we show in a mathematically rigorous way that the global ground states of the generalized antiferromagnetic Heisenberg model on a bipartite lattice with unequal sublattice points have both ferromagnetic and antiferromagnetic long-range orders with the latter being predominant. Our rigorous results conform to Neel's theory.

Journal of Physics A Mathematical and General•Apr 7, 1994•22 citations

Bifurcation of ground states and ferrimagnetic long-range order in anisotropic mixed-spin systems

Guang-Shan Tian, Hai-Qing Lin

In this paper, we study a generalized anisotropic mixed-spin ferrimagnetic Heisenberg model on an arbitrary bipartite lattice. We prove rigorously that, under some very general conditions, this model has a unique ground state with ${S}_{z}=0$ in the $\mathrm{XY}$ regime and two degenerate ground states with nonzero magnetization in the Ising regime, respectively. Therefore, the isotropic point of this model is a bifurcation point for its ground states. Furthermore, we also show that, if magnetization of the ground states in the Ising regime is a macroscopic quantity in the thermodynamic limit, then these states have both ferromagnetic and antiferromagnetic long-range order. In other words, they are ferrimagnetically ordered. These conclusions confirm the previous results derived by numerical calculations on small one-dimensional mixed-spin chains.

Physical review. B, Condensed matter•Dec 16, 2002•7 citations

Weak Form of the Griffiths Theorem for the Ferromagnetic Heisenberg Model

Robert H. T. Yeh

A weaker form of Griffiths' theorem is established for the ferromagnetic Heisenberg model.Received 18 August 1969DOI:https://doi.org/10.1103/PhysRevLett.23.1241©1969 American Physical Society

Physical Review Letters•Nov 24, 1969•6 citations

Existence of Long-Range Magnetic Order in the Ground State of Two-Dimensional Spin-1/2 Heisenberg Antiferromagnets

Martin Indergand, Manfred Sigrist

We give a rigorous proof of the existence of long-range antiferromagnetic order in the ground state of several two-dimensional spin-1/2 Heisenberg systems.Three types of systems are considered.The first type consists of an even number, N , of coupled square lattices with antiferromagnetic nearest-neighbor Heisenberg interactions.In this case, we prove the existence of long-range order (LRO) in the ground state for an interplane to inplane coupling ratio r in the range 0.16 ≤ r ≤ 2.1 for N ≥ 4. Further, we prove that the antiferromagnetic bilayer with ferromagnetic next-nearest-neighbor (nnn) interplane couplings possesses LRO in the ground state for 0.21 ≤ r < 1/4, where r is the absolute value of the ratio of the ferromagnetic and antiferromagnetic couplings.The final example consists of two antiferromagnetic spin-1/2 square lattices that are coupled via an antiferromagnetic nnn interplane coupling r.For r = 1, this system is effectively a spin-1 square lattice and has an ordered ground state.We show that LRO exists in the region 0.85 ≤ r ≤ 1. * ) Note that E r q in the notation of KLS corresponds to 2 + r -E q in our notation.

Progress of Theoretical Physics•Jan 1, 2007•2 citations

Griffiths' Theorems for the Ferromagnetic Heisenberg Model

C. A. Hurst, S. Sherman

It is shown that for the quantum mechanical Heisenberg ferromagnet, the correlation is not necessarily a monotone increasing function of interactions.Received 25 April 1969DOI:https://doi.org/10.1103/PhysRevLett.22.1357©1969 American Physical Society

Physical Review Letters•Jun 23, 1969•26 citations
In this paper, we show that for a one-dimensional antiferromagnetic Heisenberg model with unequal spins, its absolute ground state has both antiferromagnetic and ferromagnetic long-range orders.Received 24 October 1996DOI:https://doi.org/10.1103/PhysRevB.56.5355©1997 American Physical Society
The concept of ferrimagnetism was first proposed by Neel to explain why some materials have a macroscopic magnetization but no ferromagnetic long-range order, when the temperature T is lower than a phase transition temperature T c . In this article, based on a theorem of Lieb and Mattis, we show in a mathematically rigorous way that the global ground states of the generalized antiferromagnetic Heisenberg model on a bipartite lattice with unequal sublattice points have both ferromagnetic and antiferromagnetic long-range orders with the latter being predominant. Our rigorous results conform to Neel's theory.
In this paper, we study a generalized anisotropic mixed-spin ferrimagnetic Heisenberg model on an arbitrary bipartite lattice. We prove rigorously that, under some very general conditions, this model has a unique ground state with Sz=0{S}_{z}=0Sz​=0 in the XY\mathrm{XY}XY regime and two degenerate ground states with nonzero magnetization in the Ising regime, respectively. Therefore, the isotropic point of this model is a bifurcation point for its ground states. Furthermore, we also show that, if magnetization of the ground states in the Ising regime is a macroscopic quantity in the thermodynamic limit, then these states have both ferromagnetic and antiferromagnetic long-range order. In other words, they are ferrimagnetically ordered. These conclusions confirm the previous results derived by numerical calculations on small one-dimensional mixed-spin chains.
We give a rigorous proof of the existence of long-range antiferromagnetic order in the ground state of several two-dimensional spin-1/2 Heisenberg systems.Three types of systems are considered.The first type consists of an even number, N , of coupled square lattices with antiferromagnetic nearest-neighbor Heisenberg interactions.In this case, we prove the existence of long-range order (LRO) in the ground state for an interplane to inplane coupling ratio r in the range 0.16 ≤ r ≤ 2.1 for N ≥ 4. Further, we prove that the antiferromagnetic bilayer with ferromagnetic next-nearest-neighbor (nnn) interplane couplings possesses LRO in the ground state for 0.21 ≤ r < 1/4, where r is the absolute value of the ratio of the ferromagnetic and antiferromagnetic couplings.The final example consists of two antiferromagnetic spin-1/2 square lattices that are coupled via an antiferromagnetic nnn interplane coupling r.For r = 1, this system is effectively a spin-1 square lattice and has an ordered ground state.We show that LRO exists in the region 0.85 ≤ r ≤ 1. * ) Note that E r q in the notation of KLS corresponds to 2 + r -E q in our notation.