The Kauzmann Transition to an Ideal Glass Phase

TL;DR

This paper reviews the theoretical and simulation evidence for the Kauzmann transition, a hypothesized thermodynamic glass transition at a finite temperature, and discusses its relevance in finite-dimensional systems.

Contribution

It critically assesses the existence and nature of the Kauzmann transition in finite dimensions through recent simulation results and theoretical analysis.

Findings

Evidence for the Kauzmann transition in mean-field theory

Simulation results in 2D and 3D models

Discussion on the relevance of the transition in real systems

Abstract

The idea that a thermodynamic glass transition of some sort underlies the observed glass formation has been highly debated since Kauzmann first stressed the hypothetical entropy crisis that could take place if one were able to equilibrate supercooled liquids below the experimental glass transition temperature $T_g$. This a priori unreachable transition at some $T_K<T_g$ has since received a firm theoretical basis as a key feature predicted by the mean-field theory of the glass transition. In this chapter, we assess whether, and in which form, such a transition can survive in finite dimensions, and we review some of the recent computer simulation work addressing the issue in $2$- and $3$-dimensional glass-forming liquid models. We also discuss theoretical reasons to focus on an apparently inaccessible singularity.