Bypassing sluggishness: SWAP algorithm and glassiness in high dimensions

TL;DR

The paper investigates the SWAP algorithm's efficiency in high-dimensional glassy systems, revealing its diminishing speedup with increasing dimension but its ability to delay activated dynamics even in high dimensions, enabling new computational studies.

Contribution

It provides a detailed analysis of SWAP's performance across dimensions 2 to 8, showing its limitations and potential in high-dimensional glass physics.

Findings

SWAP speedup decreases rapidly with dimension

SWAP delays activated dynamics in high dimensions

Enables computational study of glassy dynamics beyond 3D

Abstract

The recent implementation of a swap Monte Carlo algorithm (SWAP) for polydisperse mixtures fully bypasses computational sluggishness and closes the gap between experimental and simulation timescales in physical dimensions $d=2$ and $3$. Here, we consider suitably optimized systems in $d=2, 3,\dots, 8$, to obtain insights into the performance and underlying physics of SWAP. We show that the speedup obtained decays rapidly with increasing the dimension. SWAP nonetheless delays systematically the onset of the activated dynamics by an amount that remains finite in the limit $d \to \infty$. This shows that the glassy dynamics in high dimensions $d>3$ is now computationally accessible using SWAP, thus opening the door for the systematic consideration of finite-dimensional deviations from the mean-field description.