Ground-State Magnetization in Disordered Systems : Exchange vs. Off-Diagonal Interaction Fluctuations

In a Hartree-Fock picture, itinerant ferromagnetism results from a competition between kinetic and exchange energy, with the magnetized state being favored at large interaction strength. In a recent paper \cite{spings} we showed that in contrast to this average effect, fluctuations of off-diagonal interaction matrix elements systematically reduce the ground-state magnetization. When the interaction dominates, the occurence of a non-zero ground-state magnetization depends on the ratio $\lambda$ between average exchange energy and the fluctuation amplitude of the off-diagonal matrix elements, and a nonzero critical value $\lambda_c$ is necessary to magnetize the ground-state. We extend these results by numerical studies of $\lambda$ for standard tight-binding models which indicate a regime of intermediate disorder where off-diagonal fluctuations should play an important role for ground-state magnetization. We also emphasize the presence of strong correlations between minimal eigenvalues of different magnetization blocks which further reduce the probability of a nonzero ground-state spin.