Mean field theory of the swap Monte Carlo algorithm

TL;DR

This paper uses mean field replica liquid theory to analyze why swap Monte Carlo accelerates glass-forming systems, showing it delays the dynamical transition compared to standard Monte Carlo, supported by numerical simulations.

Contribution

It extends the Gaussian ansatz in mean field theory to include particle exchange, providing analytical insights into the dynamical transition differences.

Findings

Swap Monte Carlo delays the dynamical transition compared to standard Monte Carlo.

Numerical simulations confirm the theoretical predictions.

The results suggest modifications to the thermodynamic theory of the glass transition.

Abstract

The swap Monte Carlo algorithm combines the translational motion with the exchange of particle species, and is unprecedentedly efficient for some models of glass former. In order to clarify the physics underlying this acceleration, we study the problem within the mean field replica liquid theory. We extend the Gaussian ansatz so as to take into account the exchange of particles of different species, and we calculate analytically the dynamical transition points corresponding to the swap and standard Monte Carlo algorithms. We show that the system evolved with the standard Monte Carlo algorithm exhibits the dynamical transition before that of the swap Monte Carlo algorithm. We also test the result by performing numerical simulations of a binary mixture of the Mari-Kurchan model, both with standard and swap Monte Carlo. This scenario provides a possible explanation for the efficiency of the swap Monte Carlo algorithm. Finally, we discuss how the thermodynamic theory of the glass transition should be modified based on our results.