Stability of ferromagnetism in Hubbard models with degenerate single-particle ground states

A Hubbard model with a N-d-fold degenerate single-particle ground state has ferromagnetic ground states ii the number of electrons is less than or equal to N-d. It is shown rigorously that the local stability of ferromagnetism in such a model implies global stability: the model has only ferromagnetic ground states, if there are no single spin-flip ground states. If the number of electrons is equal to N-d, it is well known that the ferromagnetic ground state is unique if and only if the single-particle density matrix is irreducible. We present a simplified proof for this result.