arXiv subjects

Hal Tasaki

Publications and source records attributed to Hal Tasaki.

74 records · Page 5Linked to original sources

arXiv1996

A note on ferromagnetism in the Hubbard model on the complete graph

Recently there have appeared some papers which discuss the existence of ferromagnetism in the Hubbard model defined on the complete graph. At least for the special electron number N_e=N-1, where N denotes the number of sites in the lattice, the existence of ferromagnetism in this model was established rigorously some time ago, as special (and indeed the simplest) cases of more general classes of models. Here we explain these implications to clarify the situation, although we believe the implications are straightforward. We are posting this note to the preprint archive to make it public, but we are not planning to publish it in other forms. This is because we do not think the problem warrants any extra publications, and we believe that the validity of our explanation is evident to the readers.

cond-mat↗

arXiv1993

Ferromagnetism in the Hubbard Model-- Examples from Models with Degenerate Single-Electron Ground States

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 has $N_{\rm d}$-fold degenerate ground states. The degeneracy $N_{\rm d}$ is proportional to the total number of sites $\absΛ$. We prove that the ground states of the models exhibit ferromagnetism when the electron filling factor is not more than and sufficiently close to $ρ_0=N_{\rm d}/(2\absΛ)$, 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.

cond-mat↗