### Abstract

We consider the Hubbard model on a finite set of sites with nonpositive hopping matrix elements and infinitely strong on-site repulsion. Nagaoka's theorem states that in this model the relative ground state in the sector with one unoccupied site is maximally ferromagnetic. We show that this phenomenon is a consequence of a combinatorial coincidence valid in the one-hole regime only. In the case of more than one hole there is no reason to expect maximally ferromagnetic ground states. We prove this claim for the case of two holes for models defined on a class of graphs which contains all tori that are not too small. © 1991 Kluwer Academic Publishers.

Original language | English |
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Pages (from-to) | 321-333 |

Number of pages | 13 |

Journal | Letters in Mathematical Physics |

Volume | 22 |

Issue number | 4 |

DOIs | |

Publication status | Published - Aug 1991 |

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### Keywords

- AMS subject classifications (1991): 81Q99, 81V70, 82B10

### Cite this

*Letters in Mathematical Physics*,

*22*(4), 321-333. https://doi.org/10.1007/BF00405607

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*Letters in Mathematical Physics*, vol. 22, no. 4, pp. 321-333. https://doi.org/10.1007/BF00405607

**Failure of saturated ferromagnetism for the Hubbard model with two holes.** / Tóth, Bálint.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Failure of saturated ferromagnetism for the Hubbard model with two holes

AU - Tóth, Bálint

PY - 1991/8

Y1 - 1991/8

N2 - We consider the Hubbard model on a finite set of sites with nonpositive hopping matrix elements and infinitely strong on-site repulsion. Nagaoka's theorem states that in this model the relative ground state in the sector with one unoccupied site is maximally ferromagnetic. We show that this phenomenon is a consequence of a combinatorial coincidence valid in the one-hole regime only. In the case of more than one hole there is no reason to expect maximally ferromagnetic ground states. We prove this claim for the case of two holes for models defined on a class of graphs which contains all tori that are not too small. © 1991 Kluwer Academic Publishers.

AB - We consider the Hubbard model on a finite set of sites with nonpositive hopping matrix elements and infinitely strong on-site repulsion. Nagaoka's theorem states that in this model the relative ground state in the sector with one unoccupied site is maximally ferromagnetic. We show that this phenomenon is a consequence of a combinatorial coincidence valid in the one-hole regime only. In the case of more than one hole there is no reason to expect maximally ferromagnetic ground states. We prove this claim for the case of two holes for models defined on a class of graphs which contains all tori that are not too small. © 1991 Kluwer Academic Publishers.

KW - AMS subject classifications (1991): 81Q99, 81V70, 82B10

UR - http://www.scopus.com/inward/record.url?scp=0012627676&partnerID=8YFLogxK

U2 - 10.1007/BF00405607

DO - 10.1007/BF00405607

M3 - Article

VL - 22

SP - 321

EP - 333

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 4

ER -