On the overlap between configurations in glassy liquids

TL;DR

This study explores how the definition of similarity between liquid configurations affects the phase diagram of glass-forming liquids, revealing that the critical point depends on the overlap tolerance, with implications for easier computational studies.

Contribution

It systematically analyzes the impact of overlap tolerance on the phase diagram of glassy liquids using theory and simulations, highlighting the dependence of the critical point on this parameter.

Findings

The location of glass transitions is independent of the overlap tolerance.

The critical point between low- and high-overlap phases depends on the tolerance value.

Adjusting the overlap tolerance can optimize conditions for computer simulations.

Abstract

The overlap, or similarity, between liquid configurations is at the core of the mean-field description of the glass transition, and remains a useful concept when studying three-dimensional glass-forming liquids. In liquids, however, the overlap involves a tolerance, typically of a fraction $a/\sigma$ of the inter-particle distance, associated with how precisely similar two configurations must be for belonging to the same physically relevant "state". Here, we systematically investigate the dependence of the overlap fluctuations and of the resulting phase diagram when the tolerance is varied over a large range. We show that while the location of the dynamical and thermodynamic glass transitions (if present) is independent of $a/\sigma$, that of the critical point associated with a transition between a low- and a high-overlap phases in the presence of an applied source nontrivially depends on the value of $a/\sigma$. We rationalize our findings by using liquid-state theory and the hypernetted chain (HNC) approximation for correlation functions. In addition, we confirm the theoretical trends by studying a three-dimensional glass-former by computer simulations. We show in particular that \rev{a range of $a/\sigma$ below what is commonly considered maximizes the temperature of the critical point, pushing it up in a liquid region where viscosity is low and computer investigations are easier due to a significantly faster equilibration.