Evidence of growing spatial correlations at the glass transition from nonlinear response experiments C. Crauste-Thibierge $^{1}$, C. Brun$^{1}$, F. Ladieu1 $^{⋆}$, D. L’Hˆ ote 1 $^{⋆}$, G. Biroli $^{2}$, and J-P. Bouchaud3 ∗ 1 SPEC (CNRS URA 2464), DSM/IRAMIS CEA Saclay, Bat.772, F-91191 Gif-sur-Yvette France 2 Institut de Physique Th´eorique, CEA, (CNRS URA 2306), 91191 Gif-sur-Yvette, France and 3 Science & Finance, Capital Fund Management, 6, Bd. Haussmann, 75009 Paris, France (Dated: November 26, 2018) Abstract The ac nonlinear dielectric response χ$_{3}$ ( ω, T ) of glycerol was measured close to its glass transition temperature T$_{g}$ to investigate the prediction that supercooled liquids respond in an increasingly non-linear way as the dynamics slows down (as spin-glasses do). We find that χ$_{3}$ ( ω, T ) indeed displays several non trivial features. It is peaked as a function of the frequency ω and obeys scaling as a function of ωτ ( T ), with τ ( T ) the relaxation time of the liquid. The height of the peak, proportional to the number of dynamically correlated molecules N$_{corr}$ ( T ), increases as the system becomes glassy, and χ$_{3}$ decays as a power-law of ω over several decades beyond the peak. These findings confirm the collective nature of the glassy dynamics and provide the first direct estimate of the T dependence of N$_{corr}$ . 1 arXiv:1002.0498v2 [cond-mat.soft] 31 Mar 2010 Accepted for publication in Physical Review Letters