Quantitative approximation schemes for glasses

TL;DR

This paper introduces a systematic approximation scheme based on an expansion around the infinite-dimensional solution to compute properties of glasses in low dimensions, linking liquid properties to glass characteristics.

Contribution

It develops a new approximation method that is exact in infinite dimensions and can be systematically improved for finite dimensions, bridging liquid and glass properties.

Findings

Scheme is exact as dimension approaches infinity

Allows computation of glass properties from liquid data

Can be systematically refined with additional expansion terms

Abstract

By means of a systematic expansion around the infinite-dimensional solution, we obtain an approximation scheme to compute properties of glasses in low dimensions. The resulting equations take as input the thermodynamic and structural properties of the equilibrium liquid, and from this they allow one to compute properties of the glass. They are therefore similar in spirit to the Mode-Coupling approximation scheme. Our scheme becomes exact, by construction, in dimension $d\to\infty$ and it can be improved systematically by adding more terms in the expansion.