Free energy landscape of a dense hard-sphere system

The topography of the free energy landscape in phase space of a dense hard- sphere system characterized by a discretized free energy functional of the Ramakishnan-Yussouff form is investigated numerically using a specially dev ised Monte Carlo procedure. We locate a considerable number of glassy local minima of the free energy and analyze the distributions of the free energy at a minimum and an appropriately defined phase-space "distance" between d ifferent minima. We find evidence for the existence of pairs of closely rel ated glassy minima("two-level systems"). We also investigate the way the sy stem makes transitions as it moves from the basin of attraction of a minimu m to that of another one after a start under nonequilibrium conditions. Thi s allows us to determine the effective height of free energy barriers that separate a glassy minimum from the others. The dependence of the height of free energy barriers on the density is investigated in detail. The general appearance of the free energy landscape resembles that of a putting green: relatively deep minima separated by a fairly flat structure. We discuss the connection of our results with the Vogel-Fulcher law and relate our observ ations to other work on the glass transition. [S1063-651X(99)00903-4].