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

Upper bound for spontaneous magnetization in the Hubbard model

Gang Su

Published May 1, 1994• 3 citations
Publisher

Abstract

A rigorous upper bound for the spontaneous magnetization per site of a general Hubbard model is obtained. The bound is independent of the on-site Coulomb potential ${\mathit{U}}_{\mathbf{r}}$ of the model, and is valid for arbitrary band fillings. From it one may find that the magnetic (ferromagnetic or antiferromagnetic) long-range order disappears in the atomic limit at finite temperatures.

DOI
10.1103/physrevb.49.12285

Related papers

Ferrimagnetic long-range order of the Hubbard model

Shun-Qing Shen, Zhaoming Qiu, Guang-Shan Tian

In this paper, we show rigorously that there exists the ferrimagnetic long-range order in the ground state of the positive-U Hubbard model at half filling on some bipartite lattices. When ${\mathit{N}}_{\mathit{A}}$>${\mathit{N}}_{\mathit{B}}$(${\mathit{N}}_{\mathit{A}}$ and ${\mathit{N}}_{\mathit{B}}$ are the total site numbers of two sublattices A and B), except for the ferromagnetism which was found by Lieb [Phys. Rev. Lett. 62, 1201 (1989)], there also exists the antiferromagnetic long-range order in the ground state. This result only requires U>0 and is independent of the dimension of the lattices.

Physical Review Letters•Feb 21, 1994•85 citations

Rigorous bounds on the susceptibilities of the Hubbard model

Kenn Kubo, Tatsuya Kishi

Rigorous bounds on the susceptibilities of the single-band Hubbard model which hold in all dimensions are presented. In the attractive model the spin susceptibility is bounded above by (4\ensuremath{\Vert}U\ensuremath{\Vert}${)}^{\mathrm{\ensuremath{-}}1}$ where U(0) is the on-site interaction potential. In the half-filled repulsive model on a bipartite lattice the charge and the on-site pairing susceptibilities are bounded above by ${\mathit{U}}^{\mathrm{\ensuremath{-}}1}$. The present result implies that the susceptibilities never diverge in the above mentioned circumstances and also the absence of corresponding long-range order.

Physical review. B, Condensed matter•Mar 1, 1990•46 citations

Ferromagnetism in Hubbard Models

Hal Tasaki

We present the first rigorous examples of nonsingular Hubbard models which exhibit ferromagnetism at zero temperature. The models are defined in arbitrary dimensions, and are characterized by finite-range hoppings, dispersive bands, and finite on-site Coulomb interaction $U$. The picture, which goes back to Heisenberg, that sufficiently large Coulomb interaction can revert Pauli paramagnetism into ferromagnetism has been confirmed in concrete examples.

arXiv:cond-mat/9509063•Physical Review Letters•Dec 18, 1995•130 citations

Ferromagnetism in Hubbard Models

We present the first rigorous examples of non-singular Hubbard models which exhibit ferromagnetism at zero temperature.The models are defined in arbitrary dimensions, and are characterized by finite-ranged hoppings, dispersive bands, and finite on-site Coulomb interaction U .The picture, which goes back to Heisenberg, that sufficiently large Coulomb interaction can revert Pauli paramagnetism into ferromagnetism has finally been confirmed in concrete examples.

WORLD SCIENTIFIC eBooks•Jan 1, 1999•0 citations

Bounds on ferromagnetism atT>0 in the hard-core electron lattice gas

András Sütö

In a recent paper by Aizenman and Lieb [Phys. Rev. Lett. 65, 1470 (1990)], it was reported that the Nagaoka ferromagnet preserves its ferromagnetic character at temperatures T>0 in any finite volume. It is shown here that at any T>0 the Nagaoka ferromagnet becomes a perfect paramagnet in the thermodynamic limit. By using an inequality for the free energy, this result is extended to the general case when the number of electrons per site goes to 1. At any T>0 the spontaneous magnetization m(T,\ensuremath{\rho}) tends to zero as the electron density \ensuremath{\rho} tends to 1. Thus, a rigorous upper bound on m(T,\ensuremath{\rho}) is obtained. The results are independent of the statistics.

Physical review. B, Condensed matter•Apr 1, 1991•17 citations

Metallic ferromagnetism in the Hubbard model on three coupled chains

Akinori Tanaka, Toshihiro Idogaki

We study the Hubbard model on three coupled chains which has the saturated ferromagnetic ground states in a finite range of the electron filling factor . In the case that both the single-electron band gap between the highest and lower two bands and the on-site Coulomb interaction are infinitely large, we will rigorously show that the present model exhibits ferromagnetism for 0 < <(1/3), where 0 0 (1/6) depending on the band structure. We will also give numerical results, which indicate that, even in the case that the band gap and the Coulomb interaction are not so large, the present ferromagnetism will survive for suitable electron filling factors.

Journal of Physics A Mathematical and General•Jan 1, 1999•7 citations
A rigorous upper bound for the spontaneous magnetization per site of a general Hubbard model is obtained. The bound is independent of the on-site Coulomb potential Ur{\mathit{U}}_{\mathbf{r}}Ur​ of the model, and is valid for arbitrary band fillings. From it one may find that the magnetic (ferromagnetic or antiferromagnetic) long-range order disappears in the atomic limit at finite temperatures.
In this paper, we show rigorously that there exists the ferrimagnetic long-range order in the ground state of the positive-U Hubbard model at half filling on some bipartite lattices. When NA{\mathit{N}}_{\mathit{A}}NA​>NB{\mathit{N}}_{\mathit{B}}NB​(NA{\mathit{N}}_{\mathit{A}}NA​ and NB{\mathit{N}}_{\mathit{B}}NB​ are the total site numbers of two sublattices A and B), except for the ferromagnetism which was found by Lieb [Phys. Rev. Lett. 62, 1201 (1989)], there also exists the antiferromagnetic long-range order in the ground state. This result only requires U>0 and is independent of the dimension of the lattices.
Rigorous bounds on the susceptibilities of the single-band Hubbard model which hold in all dimensions are presented. In the attractive model the spin susceptibility is bounded above by (4\ensuremath{\Vert}U\ensuremath{\Vert}${)}^{\mathrm{\ensuremath{-}}1}$ where U(0) is the on-site interaction potential. In the half-filled repulsive model on a bipartite lattice the charge and the on-site pairing susceptibilities are bounded above by ${\mathit{U}}^{\mathrm{\ensuremath{-}}1}$. The present result implies that the susceptibilities never diverge in the above mentioned circumstances and also the absence of corresponding long-range order.
We present the first rigorous examples of nonsingular Hubbard models which exhibit ferromagnetism at zero temperature. The models are defined in arbitrary dimensions, and are characterized by finite-range hoppings, dispersive bands, and finite on-site Coulomb interaction UUU. The picture, which goes back to Heisenberg, that sufficiently large Coulomb interaction can revert Pauli paramagnetism into ferromagnetism has been confirmed in concrete examples.
In a recent paper by Aizenman and Lieb [Phys. Rev. Lett. 65, 1470 (1990)], it was reported that the Nagaoka ferromagnet preserves its ferromagnetic character at temperatures T>0 in any finite volume. It is shown here that at any T>0 the Nagaoka ferromagnet becomes a perfect paramagnet in the thermodynamic limit. By using an inequality for the free energy, this result is extended to the general case when the number of electrons per site goes to 1. At any T>0 the spontaneous magnetization m(T,\ensuremath{\rho}) tends to zero as the electron density \ensuremath{\rho} tends to 1. Thus, a rigorous upper bound on m(T,\ensuremath{\rho}) is obtained. The results are independent of the statistics.
We study the Hubbard model on three coupled chains which has the saturated ferromagnetic ground states in a finite range of the electron filling factor . In the case that both the single-electron band gap between the highest and lower two bands and the on-site Coulomb interaction are infinitely large, we will rigorously show that the present model exhibits ferromagnetism for 0 < <(1/3), where 0 0 (1/6) depending on the band structure. We will also give numerical results, which indicate that, even in the case that the band gap and the Coulomb interaction are not so large, the present ferromagnetism will survive for suitable electron filling factors.