Ideal Glass Transitions by Random Pinning

TL;DR

This paper investigates how freezing a fraction of particles in a supercooled liquid induces an ideal glass transition, revealing critical properties and length scales, and offering new insights into the glass transition phenomenon.

Contribution

It introduces a mean-field phase diagram and real-space renormalization group analysis of the glass transition caused by particle pinning, connecting static length scales to the transition.

Findings

Pinning particles causes an ideal glass transition at a critical fraction c_K(T).

Critical properties are governed by two zero-temperature fixed points.

The typical distance between frozen particles relates to the static point-to-set lengthscale.

Abstract

We study the effect of freezing the positions of a fraction $c$ of particles from an equilibrium configuration of a supercooled liquid at a temperature $T$. We show that within the Random First-Order Transition theory pinning particles leads to an ideal glass transition for a critical fraction $c=c_{K}(T)$ even for moderate super-cooling, e.g. close to the Mode-Coupling transition temperature. We first derive the phase diagram in the $T-c$ plane by mean field approximations. Then, by applying a real-space renormalization group method, we obtain the critical properties for $|c-c_{K}(T)|\rightarrow 0$, in particular the divergence of length and time scales. These are dominated by two zero-temperature fixed points. We also show that for $c=c_{K}(T)$ the typical distance between frozen particles is related to the static point-to-set lengthscale of the unconstrained liquid. We discuss what are the main differences when particles are frozen in other geometries and not from an equilibrium configuration. Finally, we explain why the glass transition induced by freezing particles provides a new and very promising avenue of research to probe the glassy state and ascertain, or disprove, the validity of the theories of the glass transition.