Critical dynamical heterogeneities close to continuous second-order glass transitions
Résumé
We analyse, using Inhomogenous Mode-Coupling Theory, the critical scaling behaviour of the dynamical susceptibility at a distance $\epsilon$ from continuous second-order glass transitions. We find that the dynamical correlation length $\xi$ behaves generically as $\epsilon ^{-1/3}$ and that the upper critical dimension is equal to six. More surprisingly, we find activated dynamic scaling, where $\xi$ grows with time as ln$^2t$ exactly at criticality. All these results suggest a deep analogy between the glassy behaviour of attractive colloids or randomly pinned supercooled liquids and that of the Random Field Ising Model.