Fast Simulation of Facilitated Spin Models

TL;DR

This paper introduces an efficient simulation method for kinetically constrained models of glasses, significantly improving over standard techniques and enabling detailed studies of relaxation dynamics across multiple dimensions.

Contribution

The authors adapt Novotny's absorbing Markov chain Monte Carlo algorithm to kinetically constrained models, achieving several orders of magnitude faster simulations and broadening applicability.

Findings

Simulation times are greatly reduced compared to standard methods.

Hierarchical relaxation persists in the East model across all studied dimensions.

The method can be extended to other kinetically constrained models.

Abstract

We show how to apply the absorbing Markov chain Monte Carlo algorithm of Novotny to simulate kinetically constrained models of glasses. We consider in detail one-spin facilitated models, such as the East model and its generalizations to arbitrary dimensions. We investigate how to maximise the efficiency of the algorithms, and show that simulation times can be improved on standard continuous time Monte Carlo by several orders of magnitude. We illustrate the method with equilibrium and aging results. These include a study of relaxation times in the East model for dimensions d=1 to d=13, which provides further evidence that the hierarchical relaxation in this model is present in all dimensions. We discuss how the method can be applied to other kinetically constrained models.