Mean-field theory, mode-coupling theory, and the onset temperature in supercooled liquids.

We consider the relationship between the temperature at which averaged energy landscape properties change sharply (T(o)) and the breakdown of mean-field treatments of the dynamics of supercooled liquids. First, we show that the solution of the wave vector dependent mode-coupling equations undergoes an ergodic-nonergodic transition consistently close to T(o). Generalizing the landscape concept to include hard-sphere systems, we show that the property of inherent structures that changes near T(o) is governed more fundamentally by packing and free volume than potential energy. Lastly, we study the finite-size random orthogonal model (ROM), and show that the onset of noticeable corrections to mean-field behavior occurs at T(o). These results highlight connections between the energy landscape and mode-coupling approach to supercooled liquids, and identify which features of the relaxation of supercooled liquids are properly captured by mode-coupling theory.