  We compute the probability of positive large deviations of the free energy
per spin in mean-field Spin-Glass models. The probability vanishes in the
thermodynamic limit as $P(\Delta f) \propto \exp[-N^2 L_2(\Delta f)]$. For the
Sherrington-Kirkpatrick model we find $L_2(\Delta f)=O(\Delta f)^{12/5}$ in
good agreement with numerical data and with the assumption that typical small
deviations of the free energy scale as $N^{1/6}$. For the spherical model we
find $L_2(\Delta f)=O(\Delta f)^{3}$ in agreement with recent findings on the
fluctuations of the largest eigenvalue of random Gaussian matrices. The
computation is based on a loop expansion in replica space and the non-gaussian
behaviour follows in both cases from the fact that the expansion is divergent
at all orders. The factors of the leading order terms are obtained resumming
appropriately the loop expansion and display universality, pointing to the
existence of a single universal distribution describing the small deviations of
any model in the full-Replica-Symmetry-Breaking class.
