### Abstract

The Lieb-Mattis theorem on the absence of one-dimensional ferromagnetism is extended here from ground states to T>0 by proving, inter alia, that M the magnetization of a quantum system in a field h>0, is always less than the pure paramagnetic value M0=tanh with =1/kT. Our proof rests on a new formulation in terms of path integrals that holds in any dimension; another of its applications is that the Nagaoka-Thouless theorem on the Hubbard model also extends to T>0 in the sense that Mexceeds M0.

Original language | English (US) |
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Pages (from-to) | 1470-1473 |

Number of pages | 4 |

Journal | Physical Review Letters |

Volume | 65 |

Issue number | 12 |

DOIs | |

State | Published - Jan 1 1990 |

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

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## Cite this

Aizenman, M., & Lieb, E. (1990). Magnetic properties of some itinerant-electron systems at T>0.

*Physical Review Letters*,*65*(12), 1470-1473. https://doi.org/10.1103/PhysRevLett.65.1470