Characterising the slow dynamics of the swap Monte Carlo algorithm

TL;DR

This paper analyzes how swap Monte Carlo accelerates dynamics in supercooled liquids, revealing that it reduces kinetic constraints and dynamic heterogeneity, leading to nearly Gaussian, diffusive behavior at very low temperatures.

Contribution

It provides a detailed characterization of the slow dynamics under swap Monte Carlo, highlighting its distinct nature from local Monte Carlo and its near-optimal local equilibrium properties.

Findings

Swap dynamics are qualitatively different from local Monte Carlo.

Dynamic heterogeneity is significantly suppressed with swap moves.

Swap Monte Carlo exhibits nearly Gaussian, diffusive dynamics.

Abstract

The swap Monte Carlo algorithm introduces non-physical dynamic rules to accelerate the exploration of the configuration space of supercooled liquids. Its success raises deep questions regarding the nature and physical origin of the slow dynamics of dense liquids, and how it is affected by swap moves. We provide a detailed analysis of the slow dynamics generated by the swap Monte Carlo algorithm at very low temperatures in two glass-forming models. We find that the slowing down of the swap dynamics is qualitatively distinct from its local Monte Carlo counterpart, with considerably suppressed dynamic heterogeneity both at single-particle and collective levels. Our results suggest that local kinetic constraints are drastically reduced by swap moves, leading to nearly Gaussian and diffusive dynamics and weakly growing dynamic correlation lengthscales. The comparison between static and dynamic fluctuations shows that swap Monte Carlo is a nearly optimal local equilibrium algorithm, suggesting that further progress should necessarily involve collective or driven algorithms.