Fifth-order susceptibility unveils growth of thermodynamic amorphous order in glass-formers.

Glasses are ubiquitous in daily life and technology. However the microscopic mechanisms generating this state of matter are still controversially debated: glasses are considered either as merely hyper-viscous liquids or as resulting from a genuine thermodynamic phase transition towards a rigid state. We show that third and fifth order susceptibilities provide a smoking-gun answer to this longstanding controversy. Performing the corresponding high-precision nonlinear dielectric experiments for supercooled glycerol and propylene carbonate, we find strong support for theories based upon thermodynamic amorphous order. Moreover, when lowering temperature, we find that the growing transient domains are compact, i.e. their fractal dimension d_f = 3. The glass transition may thus represent a new class of critical phenomena, different from canonical second-order phase transitions for which d_f < 3. Time permitting, I will shortly review some experimental results obtained recently in spin glasses and in colloids, explaining why nonlinear responses directly test amorphous order in glassy matter.