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

The supercooled N3 model exhibits an increasingly slow dynamics as density approaches the random closest packing density. Here, we present a direct measurement of the dynamical correlation function G4(r,t), showing the emergence of a growing length scale ξ(4) across which the dynamics is correlated. The correlation length measured, up to 120 lattice sites, power law diverges as the density approaches ρ(t), the density at which the fluid phase of the model is predicted to terminate. The four-point susceptibility, often used as an agent to estimate ξ(4), does not depend simply on the latter. Rather, it depends strongly on the short-range behavior of G4(r,t). Consequently, χ(4) peaks before ξ(4) reaches its maximal value. The two quantities should therefore be studied independently.