Abstract
swap algorithms can shift the glass transition to lower temperatures, a recent unexplained observation constraining the nature of this phenomenon. Here we show that swap dynamics is governed by an effective potential describing both particle interactions as well as their ability to change size. Requiring its stability is more demanding than for the potential energy alone. This result implies that stable configurations appear at lower energies with swap dynamics, and thus at lower temperatures when the liquid is cooled. The magnitude of this effect is predicted to be proportional to the width of the radii distribution, and to decrease with compression for finite-range purely repulsive interaction potentials. We test these predictions numerically and discuss the implications of our findings for the glass transition. These results are extended to the case of hard spheres where swap is argued to destroy metastable states of the free energy coarse grained on vibrational timescales. Our analysis unravels the soft elastic modes responsible for the speed-up induced by swap, and allows us to predict the structure and the vibrational properties of glass configurations reachable with swap. In particular, for continuously polydisperse systems we predict the jamming transition to be dramatically altered, as we confirm numerically. A surprising practical outcome of our analysis is a new algorithm that generates ultrastable glasses by a simple descent in an appropriate effective potential.
- Received 16 April 2018
- Revised 28 June 2018
DOI:https://doi.org/10.1103/PhysRevX.8.031050
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Typically, when a liquid cools below its freezing point, it forms a crystalline solid. But if the temperature decreases fast enough, the liquid forms a disordered solid, known as a glass instead. The physics underlying this process is not well understood. Competing theories are difficult to disprove, and the requisite algorithms are computationally expensive. Recently, researchers made a considerable advance by developing an algorithm where particles of different radii can swap positions, in addition to the usual moves of particle positions. This approach decreases the temperature of the glass transition and improves simulations, though it is not clear why. Here we provide an explanation for the success of this algorithm.
We show that the swap dynamics can be mapped into an effective potential, where the radii of particles can vary continuously. This extra degree of freedom generates softer elementary excitations compared to the usual dynamics where the radii are fixed. These soft excitations, in turn, destroy the inherent structures of the usual potential-energy landscape, thus explaining why the particle swaps lower the glass transition temperature and why the dynamics near the transition accelerate.
A surprising practical outcome of our work is a new algorithm that generates ultrastable glasses by descending along the effective potential.
