Suppression of ground-state magnetization in finite-size systems due to off-diagonal interaction fluctuations

We study a generic model of interacting fermions in a finite-size disordered system. We show that the off-diagonal interaction matrix elements induce density of state fluctuations which generically favor a minimum spin ground state at large interaction amplitude, U. This effect competes with the exchange effect which favors large magnetization at large U, and it suppresses this exchange magnetization in a large parameter range. When off-diagonal fluctuations dominate, the model predicts a spin gap which is larger for odd-spin ground states as for even spin, suggesting a simple experimental signature of this off-diagonal effect in Coulomb blockade transport measurements.