Equilibrium phase diagram of a randomly pinned glass-former

TL;DR

This study uses computer simulations to map the equilibrium phase diagram of a glass-former with randomly frozen particles, identifying key transition temperatures and their relation to the energy landscape, supporting the random first order transition theory.

Contribution

It provides the first direct equilibrium determination of the Kauzmann temperature in a pinned glass-former without extrapolation, linking thermodynamic and overlap-based transition lines.

Findings

The transition line from thermodynamic integration matches the overlap distribution.

The Kauzmann and dynamic transition temperatures cross at a finite fraction of pinned particles.

The energy landscape analysis reveals the dependence of saddle points on temperature and pinning fraction.

Abstract

We use computer simulations to study the thermodynamic properties of a glass former in which a fraction $c$ of the particles has been permanently frozen. By thermodynamic integration, we determine the Kauzmann, or ideal glass transition, temperature $T_K(c)$ at which the configurational entropy vanishes. This is done without resorting to any kind of extrapolation, {\it i.e.}, $T_K(c)$ is indeed an equilibrium property of the system. We also measure the distribution function of the overlap, {\it i.e.}, the order parameter that signals the glass state. We find that the transition line obtained from the overlap coincides with that obtained from the thermodynamic integration, thus showing that the two approaches give the same transition line. Finally we determine the geometrical properties of the potential energy landscape, notably the $T-$and $c-$dependence of the saddle index and use these properties to obtain the dynamic transition temperature $T_d(c)$. The two temperatures $T_K(c)$ and $T_d(c)$ cross at a finite value of $c$ and indicate the point at which the glass transition line ends. These findings are qualitatively consistent with the scenario proposed by the random first order transition theory.