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

In: Inequalities

Author

Listed:
  • Elliott H. Lieb

    (Princeton University, Department of Physics and Mathematics)

  • Michael Aizenman

    (New York University, Courant Institute of Mathematical Sciences)

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 ).

Suggested Citation

  • Elliott H. Lieb & Michael Aizenman, 2002. "Magnetic Properties of Some Itinerant-Electron Systems at T > 0," Springer Books, in: Michael Loss & Mary Beth Ruskai (ed.), Inequalities, pages 95-98, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-55925-9_10
    DOI: 10.1007/978-3-642-55925-9_10
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