| Mode-Coupling Theory (MCT) is conjectured to be a mean field description of dynamics of supercooled liquids and the replica theory is a static (thermodynamic) counterpart. This mean-field scenario was inspired by a mean-field models of spin-glasses. According this scenario MCT's nonergodic transition point should be identified with a dynamic transition point which the replica theory predicts. We shall report that the standard MCT for liquids is not consistent with this scenario. Our claim is based on studies of the glass transition in dimensions higher than three. We observed the following; (i) Simulation study for a monatomic hard sphere fluid in d=4 demonstrates that dynamic heterogeneities are reduced and MCT works better than lower-dimensional systems, (ii) for d=3 and 4, MCT's predictions in general agree better with simulation results than the replica theory, but (iii) MCT falters in higher dimensions and predicts spurious dimension dependence of the transition points distinct from those of the replica theory. These results raise more questions than answers on the mean field scenario of the structural glass transition. |
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