Non-linear susceptibility in glassy systems: a probe for cooperative dynamical length scales

TL;DR

This paper links non-linear susceptibility measurements to cooperative length scales in glassy systems, providing a method to probe heterogeneity and growth of cooperativity as systems approach a critical point.

Contribution

It establishes a theoretical connection between non-linear response functions and four-point correlations in glassy systems, enabling experimental access to cooperative length scales.

Findings

Non-linear susceptibility increases with the growth of cooperative length.

Theoretical analysis is exact within Mode-Coupling Theory.

Provides a method to measure heterogeneity in glassy dynamics.

Abstract

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.