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Magnetic Properties of Some Itinerant-Electron Systems at T > 0

  • Elliott H. Lieb
  • Michael Aizenman
Chapter

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(ß,h), the magnetization of a quantum system in a field h> 0, is always less than the pure paramagnetic value M o(ß,h)=lanh(ßh), with ß=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 M(ß,h ) exceeds M 0(ß,h ).

Keywords

Hubbard Model World Line Physical Review Letter Wiener Measure Spin Assignment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Note

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Elliott H. Lieb
    • 2
  • Michael Aizenman
    • 1
  1. 1.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA
  2. 2.Department of Physics and MathematicsPrinceton UniversityPrincetonUSA

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