  Interacting spinning fermions with strong quasi-random disorder are analyzed
via rigorous Renormalization Group (RG) methods combined with KAM techniques.
The correlations are written in terms of an expansion whose convergence follows
from number-theoretical properties of the frequency and cancellations due to
Pauli principle. A striking difference appears between spinless and spinning
fermions; in the first case there are no relevant effective interactions while
in presence of spin an additional relevant quartic term is present in the RG
flow. The large distance exponential decay of the correlations present in the
non interacting case, consequence of the single particle localization, is shown
to persist in the spinning case only for temperatures greater than a power of
the many body interaction, while in the spinless case this happens up to zero
temperature.
