Fractal free energy landscapes in structural glasses

TL;DR

This paper reveals that the free energy landscape of structural glasses becomes fractal deep in the glass, leading to a rougher landscape with critical properties that unify glass and jamming physics.

Contribution

It introduces the concept of a fractal free energy landscape in glasses, connecting jamming transition properties with glass theory through analytical and numerical evidence.

Findings

Identification of a roughness transition to fractal basins in glasses

Analytical determination of critical exponents at jamming

Compatibility of results with numerical simulations

Abstract

Glasses are amorphous solids whose constituent particles are caged by their neighbors and thus cannot flow. This sluggishness is often ascribed to the free energy landscape containing multiple minima (basins) separated by high barriers. Here we show, using theory and numerical simulation, that the landscape is much rougher than is classically assumed. Deep in the glass, it undergoes a "roughness transition" to fractal basins. This brings about isostaticity at jamming and marginality of glassy states near jamming. Critical exponents for the basin width, the weak force distribution, and the spatial spread of quasi-contacts at jamming can be analytically determined. Their value is found to be compatible with numerical observations. This advance therefore incorporates the jamming transition of granular materials into the framework of glass theory. Because temperature and pressure control which features of the landscape are experienced, glass mechanics and transport are expected to reflect the features of the topology we discuss here. Hitherto mysterious properties of low-temperature glasses could be explained by this approach.