Direct measurements of the dynamical correlation length indicate its divergence at an athermal glass transition

TL;DR

This study directly measures the dynamical correlation length in a super-cooled model, revealing its divergence at an athermal glass transition, and highlights the importance of analyzing correlation functions separately from susceptibility.

Contribution

It provides the first direct measurement of the dynamical correlation length in the super-cooled N3 model and clarifies its relationship with four-point susceptibility.

Findings

Correlation length $\xi_4$ diverges as density approaches $ ho_t$

Four-point susceptibility $\xi_4$ depends on short-range behavior of $G_4(r,t)$

$\xi_4$ peaks after $ ext{chi}_4$, indicating independent analysis needed

Abstract

The super-cooled $N3$ model exhibits an increasingly slow dynamics as density approaches the model's random closest packing density. Here, we present a direct measurement of the dynamical correlation function $G_4(r,t)$, showing the emergence of a growing length scale $\xi_4$ across which the dynamics is correlated. The correlation length measured, up to 120 lattice sites, power-law diverges as the density approaches $\rho_t$, the density at which the fluid phase of the model is predicted to terminate. It is shown that the four-point susceptibility, often used as an agent to estimate $\xi_4$, does not depend simply on the latter. Rather, it depends strongly on the short-range behavior of $G_4(r,t)$. Consequently, $\chi_4$ peaks before $\xi_4$ reaches its maximal value. The two quantities should therefore be studied independently.