  We investigate the spin structure of many-fermion systems with a
spin-conserving two-body random interaction. We find a strong dominance of
spin-0 ground states and considerable correlations between energies and wave
functions of low-lying states with different spin, but no indication of
pairing. The spectral densities exhibit spin-dependent shapes and widths, and
depend on the relative strengths of the spin-0 and spin-1 couplings in the
two-body random matrix. The spin structure of low-lying states can largely be
explained analytically.
