Emergence of cooperative dynamics in fully packed classical dimers

Oakes, Tom; Garrahan, Juan P.; Powell, Stephen

Abstract

We study the behavior of classical dimer coverings of the square lattice—a paradigmatic model for systems subject to constraints—evolving under local stochastic dynamics, by means of Monte Carlo simulations and theoretical arguments. We observe clear signatures of correlated dynamics in both global and local observables and over a broad range of time scales, indicating a breakdown of the simple continuum description that approximates well the statics. We show that this collective dynamics can be understood in terms of one-dimensional “strings” of high mobility, which govern both local and long-wavelength dynamical properties. We introduce a coarse-grained description of the strings, based on the Edwards–Wilkinson model, which leads to exact results in the limit of low string density and provides a detailed qualitative understanding of the dynamics in all flux sectors. We discuss the implications of our results for the dynamics of constrained systems more generally.

Citation

Oakes, T., Garrahan, J. P., & Powell, S. (2016). Emergence of cooperative dynamics in fully packed classical dimers. Physical Review E, 93(3), Article 032129. https://doi.org/10.1103/PhysRevE.93.032129

• Journal Article Type: Article
• Acceptance Date: Feb 26, 2016
• Online Publication Date: Mar 16, 2016
• Publication Date: Mar 16, 2016
• Deposit Date: Jul 7, 2016
• Publicly Available Date: Jul 7, 2016
• Journal: Physical Review E
• Print ISSN: 2470-0045
• Electronic ISSN: 2470-0053
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 93
• Issue: 3
• Article Number: 032129
• DOI: https://doi.org/10.1103/PhysRevE.93.032129
• Public URL: https://nottingham-repository.worktribe.com/output/780131
• Publisher URL: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.93.032129
• Additional Information: Emergence of cooperative dynamics in fully packed classical dimers, Tom Oakes, Juan P. Garrahan, and Stephen Powell, Phys. Rev. E 93, 032129.
• Contract Date: Jul 7, 2016