The Static Lengthscale Characterizing the Glass Transition at Lower Temperatures

TL;DR

This study investigates the static lengthscale associated with the glass transition at very low temperatures, demonstrating that swap Monte Carlo techniques effectively extend the measurable range, revealing significant growth in the lengthscale.

Contribution

The paper introduces and validates the use of swap Monte Carlo methods to measure the static lengthscale at lower temperatures than previously possible.

Findings

Swap Monte Carlo extends accessible lengthscale measurements.

The lengthscale grows with relaxation time over 15 orders of magnitude.

Vapor deposition does not aid in reaching lower temperatures.

Abstract

The existence of a static lengthscale that grows in accordance with the dramatic slowing down observed at the glass transition is a subject of intense interest. A recent publication compared two proposals for this length scale, one 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. The conclusion was that both approaches lead to the same lengthscale, but the former is easier to measure at higher temperatures and the latter at lower temperatures. But even after using both methods together, the range of increase in the observed lengthscales was limited by the relaxation times reachable by standard molecular dynamics techniques (i.e. about 4-5 orders of magnitude). In this paper we therefore attempt to explore the typical scale at even lower temperatures, testing for this purpose two approaches, one based on the idea of vapor deposition and the other on a swap Monte Carlo technique. We conclude that the first approach does not help in getting to lower temperatures, but the second one does so quite effectively. We can reach a typical lengthscale that grows in accordance with at least $15$ orders of magnitude increase in the relaxation time, competing with the best experimental conditions. We conclude by discussing the relationship between the observed lengthscale and various models of the relaxation time.