Numerical studies of Hubbard clusters: exact diagonalization and Monte-Carlo simulation

We present results of the exact diagonalization of the Hubbard model in clusters of 4,s and 6 sites by increasing the prirnitive tetrahedral cell and obeying the f.c.c. lattice symmetries. Ground state properties such as the energy spectrum, the total spin of the cluster and spin pairing correlation functions have been calculated and a magnetic phase diagram is reported. We also present exact diagonalization and numerical simula- tion results for an almost one-dimenional system which, we believe, is the simplest periodic lattice to exhibit ferromagnetism in a half-Uled band in agreement with a recent theorem by Lieb.