  We present a complete characterization of the fluctuations and correlations
of the squared overlap in the Edwards-Anderson Spin-Glass model in zero field.
The analysis reveals that the energy-energy correlations (and thus the specific
heat) have a different critical behavior than the fluctuations of the link
overlap in spite of the fact that the average energy and average link overlap
have the same critical properties. More precisely the link-overlap fluctuations
are larger than the specific heat according to a computation at first order in
the $6-\epsilon$ expansion. An unexpected outcome is that the link-overlap
fluctuations have a subdominant power-law contribution characterized by an
anomalous logarithmic prefactor which is missing in the specific heat. In order
to compute the $\epsilon$ expansion we consider the problem of the
renormalization of quadratic composite operators in a generic multicomponent
cubic field theory: the results obtained have a range of applicability beyond
spin-glass theory.
