Communications in Mathematical Physics

, Volume 158, Issue 2, pp 341–371 | Cite as

Ferromagnetism in the Hubbard model

Examples from models with degenerate single-electron ground states
  • Andreas Mielke
  • Hal Tasaki


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 hasNd-fold degenerate ground states. The degeneracyNd 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=Nd/(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.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Open Problem 
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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Andreas Mielke
    • 1
  • Hal Tasaki
    • 2
  1. 1.Institut für Theoretische PhysikUniversität HeidelbergHeidelbergGermany
  2. 2.Department of PhysicsGakushuin UniversityTokyoJapan

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