Abstract
The Hubbard model has been attracting considerable interest in physics community. In short, the Hubbard model is an “over simplified” model of electrons in a solid, which takes into account the itinerant nature of electrons and the short range Coulomb interaction between them. Like all the other “good models” in physics, the simplicity of the definition does not imply the model is easy to solve or understand. Even on heuristic levels, it is not yet clear which phenomena observed in the real itinerant elec- tron systems can be reproduced within the Hubbard model1. Rigorous results directed to such physical questions should be welcome, but are still very rare. In the present note, we will describe our recent attempts to understand mechanisms underlying the well-known phenomena of ferromagnetism2 . The main topic is the recent first rigorous example of three dimensional itinerant electron ferromagnetism which is stable under fluctuation of the electron density [27, 20].
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Tasaki, H. (1994). Ferromagnetism in Itinerant Electron Systems: Rigorous Examples from Flat-Band Hubbard Models. In: Fannes, M., Maes, C., Verbeure, A. (eds) On Three Levels. NATO ASI Series, vol 324. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2460-1_3
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