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 ξ₄ 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 ξ₄, does not depend simply on the latter. Rather, it depends strongly on the short-range behavior of G₄(r,t). Consequently, χ₄ peaks before ξ₄ reaches its maximal value. The two quantities should therefore be studied independently.