Ferromagnetism in an Itinerant Electron Cluster

In the present paper, we study the existence of metallic ferromagetism in a cluster of nanometer scale,which is described by the Hubbard inodel defined on a complete graph. Therefore, the system is highly frustrated witdrespect to electron hopping. By solving the model exactly,we show that its ground stste is fully spin-polarized athalf-filling, even if the Coulomb interaction is finite. This conclusion is in sharp contrast to the well-known result forthe Hubbard model on a bipartite lattice. As a reult, our exact solution strongly suggests that frustration may play animportant role in causing metallic ferromagnetism.