  We argue that for generic systems close to a critical point, an extended
Fluctuation-Dissipation relation connects the low frequency non-linear (cubic)
susceptibility to the four-point correlation function. In glassy systems, the
latter contains interesting information on the heterogeneity and cooperativity
of the dynamics. Our result suggests that if the abrupt slowing down of glassy
materials is indeed accompanied by the growth of a cooperative length ell, then
the non-linear, 3 omega response to an oscillating field should substantially
increase and give direct information on the temperature (or density) dependence
of ell. The analysis of the non-linear compressibility or the dielectric
susceptibility in supercooled liquids, or the non-linear magnetic
susceptibility in spin-glasses, should give access to a cooperative length
scale, that grows as the temperature is decreased or as the age of the system
increases. Our theoretical analysis holds exactly within the Mode-Coupling
Theory of glasses.
