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.