Spatial correlations in glass-forming liquids across the mode-coupling crossover

We discuss a novel approach, the point-to-set correlation functions, that allows to determine relevant static and dynamic length scales in glass-forming liquids. We find that static length scales increase monotonically when the temperature is lowered, whereas the measured dynamic length scale shows a maximum around the critical temperature of mode-coupling theory. We show that a similar non-monotonicity is found in the temperature evolution of certain finite size effects in the relaxation dynamics. These two independent sets of results demonstrate the existence of a change in the transport mechanism when the glass-former is cooled from moderately to deeply supercooled states across the mode-coupling crossover and clarify the status of the theoretical calculations done at the mean field level.