Emergence of cooperative dynamics in fully packed classical dimers

TL;DR

This paper investigates the complex cooperative dynamics of classical dimer coverings on a square lattice, revealing string-like excitations and a coarse-grained Edwards-Wilkinson model that explains their behavior across different flux sectors.

Contribution

It introduces a string-based coarse-grained model for classical dimer dynamics, providing new insights into constrained systems' collective behavior.

Findings

Identification of high-mobility strings governing dynamics

Development of an Edwards-Wilkinson based coarse-grained description

Exact results in low string density limit

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.