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It is widely believed that the emergence of slow glassy dynamics is encodedin a material's microstructure. First-principles theory [mode-coupling theory(MCT)] is able to predict the dramatic slowdown of the dynamics from onlystatic two-point correlations as input, yet it cannot capture all of theobserved dynamical behavior. Here we go beyond two-point spatial correlationfunctions by extending MCT systematically to include higher-order static anddynamic correlations. We demonstrate that only adding the static triplet directcorrelations already qualitatively changes the predicted glass-transitiondiagram of binary hard spheres and silica. Moreover, we find a non-trivialcompetition between static triplet correlations that work to stabilize theglass state, and dynamic higher-order correlations which destabilize it forboth materials. We conclude that the conventionally neglected static tripletdirect correlations as well as higher-order dynamic correlations are in factnon-negligible in both fragile and strong glassformers.

Many-body correlations are non-negligible in both fragile and strong glassformers