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The ac nonlinear dielectric response $\chi_3(\omega,T)$ of glycerol wasmeasured close to its glass transition temperature $T_g$ to investigate theprediction that supercooled liquids respond in an increasingly non-linear wayas the dynamics slows down (as spin-glasses do). We find that$\chi_3(\omega,T)$ indeed displays several non trivial features. It is peakedas a function of the frequency $\omega$ and obeys scaling as a function of$\omega \tau(T)$, with $\tau(T)$ the relaxation time of the liquid. The heightof the peak, proportional to the number of dynamically correlated molecules$N_{corr}(T)$, increases as the system becomes glassy, and $\chi_3$ decays as apower-law of $\omega$ over several decades beyond the peak. These findingsconfirm the collective nature of the glassy dynamics and provide the firstdirect estimate of the $T$ dependence of $N_{corr}$.

Evidence of growing spatial correlations at the glass transition from nonlinear response experiments