Abstract
In this paper, we discuss theoretically the behaviour of the four-point non-linear susceptibility and its associated correlation lengthfor supercooled liquids close to the mode-coupling instabilitytemperature Tc. We work in the theoretical framework of theglass transition as described by mean-field theory of disorderedsystems, and the hypernetted-chain approximation. Our results givean interpretation framework for recent numerical findings onheterogeneities in supercooled liquid dynamics.
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