Comparison of Static Length-Scales Characterizing the Glass Transition

TL;DR

This paper compares two different methods for measuring static length scales related to the glass transition, providing numerical evidence that they may identify the same underlying length scale and discussing the implications of this finding.

Contribution

It demonstrates that point-to-set and Hessian eigenvalue-based length scales may be equivalent, offering new insights into static length scales in glass transition studies.

Findings

The two methods yield similar length scales.

Numerical evidence supports their potential equivalence.

Raises theoretical questions about the fundamental relationship.

Abstract

The dramatic dynamic slowing down associated with the glass transition is considered by many to be related to the existence of a static length scale that grows when temperature decreases. Defining, identifying and measuring such a length is a subtle and non-trivial problem. Recently, two proposals, based on very different insights regarding the relevant physics, were put forward. One approach is based on the point-to-set correlation technique and the other on the scale where the lowest eigenvalue of the Hessian matrix becomes sensitive to disorder. In this Letter we present numerical evidence that the two approaches might result in the same identical length scale. This provides further mutual support to their relevance and, at the same time, raise interesting theoretical questions, discussed in the conclusion, concerning the fundamental reason for their relationship.