Fluctuations and Shape of Cooperative Rearranging Regions in Glass-Forming Liquids

Abstract

We develop a theory of amorphous interfaces in glass-forming liquids. We show that the statistical properties of these surfaces, which separate regions characterized by different amorphous arrangements of particles, coincide with the ones of domain walls in the random field Ising model. A major consequence of our results is that supercooled liquids are characterized by two different static lengths: the point-to-set ξ_{PS}, which is a measure of the spatial extent of cooperative rearranging regions, and the wandering length ξ_{⊥}, which is related to the fluctuations of their shape. We find that ξ_{⊥} grows when approaching the glass transition but slower than ξ_{PS}. The wandering length increases as s_{c}^{-1/2}, where s_{c} is the configurational entropy. Our results strengthen the relationship with the random field Ising model found in recent works. They are in agreement with previous numerical studies of amorphous interfaces and provide a theoretical framework for explaining numerical and experimental findings on pinned particle systems and static lengths in glass-forming liquids.