On non-linear susceptibility in supercooled liquids

In this paper, we discuss theoretically the behaviour of the four-point non -linear susceptibility and its associated correlation length for supercoole d liquids close to the mode-coupling instability temperature T-c. We work i n the theoretical framework of the glass transition as described by mean-fi eld theory of disordered systems, and the hypernetted-chain approximation. Our results give an interpretation framework for recent numerical findings on heterogeneities in supercooled liquid dynamics.