Free energy landscape in a dense hard sphere system

TL;DR

This study numerically explores the free energy landscape of a dense hard sphere system, revealing numerous glassy minima, two-level systems, and the density dependence of free energy barriers, providing insights into the glass transition.

Contribution

It introduces a numerical analysis of the free energy landscape in a dense hard sphere system using a discretized functional and Monte Carlo methods, identifying glassy minima and barrier structures.

Findings

Existence of numerous glassy minima and two-level systems.

Free energy barriers increase with density.

Landscape resembles a putting green with deep minima and flat regions.

Abstract

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 Ramakrishnan-Yussouff form is investigated numerically using a ``microcanonical'' 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 different minima. We find evidence for the existence of pairs of closely related glassy minima (``two-level systems''). We also investigate the way the system makes transitions as it moves from the basin of attraction of a minimum to that of another one after a start under nonequilibrium conditions. This 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 observations to other work on the glass transition.