Magnetic Properties of Some Itinerant-Electron Systems at T > 0
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 ).
KeywordsHubbard Model World Line Physical Review Letter Wiener Measure Spin Assignment
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