Abstract
After decades of research, a clear picture of the glass transition phenomenon, common to scores of different materials (molecular glasses, polymers, colloids) is still lacking. Recent theoretical works suggest the existence of dynamic criticality and growing dynamic lengthscales associated to the dynamic slowing down. Various experiments support this view but in a rather indirect manner. We will discuss the physical mechanisms leading to such a growing length scale and define multi-point dynamic susceptibilities quantifying the cooperative dynamics of glass-forming materials that are accessible to experiments, and present some recent experiments supporting these ideas.