Growing correlation length on cooling below the onset of caging in a simulated glass-forming liquid

We present a calculation of a fourth-order, time-dependent density correlation function that measures higher-order spatiotemporal correlations of the density of a liquid. From molecular dynamics simulations of a glass-forming Lennard-Jones liquid, we find that the characteristic length scale of this function has a maximum as a function of time which increases steadily beyond the characteristic length of the static pair correlation function g(r) in the temperature range approaching the mode coupling temperature from above. This length scale provides a measure of the spatially heterogeneous nature of the dynamics of the liquid in the alpha-relaxation regime.