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The mode-coupling theory of the glass transition treats the dynamics ofsupercooled liquids in terms of two-point density correlation functions. Herewe consider a generalized, hierarchical formulation of schematic mode-couplingequations in which the full basis of multipoint density correlations is takeninto account. By varying the parameters that control the effectivecontributions of higher-order correlations, we show that infinite hierarchiescan give rise to both sharp and avoided glass transitions. Moreover, smallchanges in the form of the coefficients result in different scaling behaviorsof the structural relaxation time, providing a means to tune the fragility inglass-forming materials. This demonstrates that the infinite-order construct ofgeneralized mode-coupling theory constitutes a powerful and unifying frameworkfor kinetic theories of the glass transition.

Relaxation Patterns in Supercooled Liquids from Generalized Mode-Coupling Theory