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

TL;DR

This paper develops a theoretical framework for amorphous interfaces in glass-forming liquids, linking their properties to the random field Ising model and identifying two key static lengths that characterize the glass transition.

Contribution

It introduces a theory connecting amorphous interface properties with the random field Ising model and identifies two static lengths, $\xi_{PS}$ and $\xi_ot$, describing cooperative regions and their fluctuations.

Findings

The wandering length $\xi_ot$ grows slower than $\xi_{PS}$ approaching the glass transition.

$\xi_ot$ increases as $s_c^{-1/2}$ with the configurational entropy.

Results align with numerical studies and enhance understanding of static lengths 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 super-cooled liquids are characterized by two different static lengths: the point-to-set $\xi_{PS}$ which is a measure of the spatial extent of cooperative rearranging regions and the wandering length $\xi_\perp$ which is related to the fluctuations of their shape. We find that $\xi_\perp$ grows when approaching the glass transition but slower than $\xi_{PS}$. 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.