Abstract
Whether spin-independent Coulomb interaction can be the origin of a realistic ferromagnetism in an itinerant electron system has been an open problem for a long time. Here we study a class of Hubbard models on decorated lattices, which have a special property that the corresponding single-electron Schrödinger equation hasN d-fold degenerate ground states. The degeneracyN d is proportional to the total number of sites |Λ|. We prove that the ground states of the models exhibit ferromagnetism when the electron filling factor is not more than and sufficiently close toϱ=N d/(2|Λ|), and paramagnetism when the filling factor is sufficiently small. An important feature of the present work is that it provides examples of three dimensional itinerant electron systems which are proved to exhibit ferromagnetism in a finite range of the electron filling factor.
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Aizenman, M., Lieb, E.H.: Phys. Rev. Lett.65, 1470 (1990)
Bloch, F.: Z. Phys.57, 545 (1929)
Dopf, G., Wagner, J., Dietrich, P., Muramatsu, A., Hanke, W.: Helv. Phys. Acta65, 257 (1992)
Douçot, B., Wen, X.G.: Phys. Rev. B40, 2719 (1989)
Ghosh, D.K.: Phys. Rev. Lett.27, 1584 (1971)
Griffiths, R.B.: In: Phase transitions and critical phenomena 1, Dombs, C., Green, M.S. (eds.) New York: Academic Press 1972
Grimmett, G.: Percolation. Berlin, Heidelberg, New York: Springer 1989
Heisenberg, W.J.: Z. Phys.49, 619 (1928)
Herring, C.: In: Magnetism IIB. Rado, G.T., Suhl, H. (eds.) New York, London: Academic Press 1966
Herring, C.: In: Magnetism IV. Rado, G.T., Suhl, H. (eds.) New York, London: Academic Press 1966
Hubbard, J.: Proc. Roy. Soc. (London) A276, 238 (1963)
Janiš, V., Mašek, J., Vollhardt, D.: Preprint
Kanamori, J.: Prog. Theor. Phys.30, 275 (1963)
Koma, T., Tasaki, H.: Phys. Rev. Lett.68, 3248 (1992)
Kusakabe, K., Aoki, H.: J. Phys. Soc. Jpn.61, 1165 (1992)
Kusakabe, K., Aoki, H.: Proceedings for 20th International Conference on Low Temperature Physics. To appear in Physica B, and preprint
Lieb, E.H.: In: Phase transitions. Proceedings of the fourteenth Solvay conference. New York: Wiley, Interscience 1971, p. 45
Lieb, E.H.: Phys. Rev. Lett.62, 1201 (1989)
Lieb, E.H., Mattis, D.: Phys. Rev.125, 164 (1962)
Mielke, A.: J. Phys. A: Math. Gen.24, L73 (1991)
Mielke, A.: J. Phys. A: Math. Gen.24, 3311 (1991)
Mielke, A.: J. Phys. A: Math. Gen.25, 4335 (1992)
Mielke, A.: Phys. Lett. A174, 443 (1993)
Nagaoka, Y.: Phys. Rev.147, 392 (1966)
Shastry, B.S., Krishnamurthy, H.R., Anderson, P.W.: Phys. Rev. B41, 2375 (1990)
Slater, J.C., Statz, H., Koster, G.F.: Phys. Rev.91, 1323 (1953)
Sütő, A.: Phys. Rev. B43, 8779 (1991)
Sütő, A.: Commun. Math. Phys.140, 43 (1991)
Tasaki, H.: Phys. Rev. B40, 9192 (1989)
Tasaki, H.: Phys. Rev. Lett69, 1608 (1992)
Thouless, D.J.: Proc. Phys. Soc. Lond.86, 893 (1965)
Tóth, B.: Lett. Math. Phys.22, 321 (1991)
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Mielke, A., Tasaki, H. Ferromagnetism in the Hubbard model. Commun.Math. Phys. 158, 341–371 (1993). https://doi.org/10.1007/BF02108079
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DOI: https://doi.org/10.1007/BF02108079