Fast Simulation of Facilitated Spin 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.

8 pages, 4 figures

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Cited by in corpus (11)

• Corresponding States of Structural Glass Formers
• Aspects of non-equilibrium in classical and quantum systems: slow relaxation and glasses, dynamical large deviations, quantum non-ergodicity, and open quantum dynamics
• Corresponding States of Structural Glass Formers. II
• Dimensional Study of the Caging Order Parameter at the Glass Transition
• Dimensional dependence of the Stokes--Einstein relation and its violation
• Front propagation versus bulk relaxation in the annealing dynamics of a kinetically constrained model of ultrastable glasses
• Fluctuation-dissipation relations in plaquette spin systems with multi-stage relaxation
• Using the s-Ensemble to Probe Glasses Formed by Cooling and Aging
• Theory for Glassy Behavior of Supercooled Liquid Mixtures
• The influence of dimension on the relaxation process of East-like models
• Study of the upper-critical dimension of the East model through the breakdown of the Stokes-Einstein relation