Dynamic correlations in an ordered c(2$\times$2) lattice gas

TL;DR

This paper derives and solves kinetic equations for dynamic correlations in a low-defect ordered lattice gas, revealing defect-driven fluctuations and improving upon previous diffusion-based models, with results validated by simulations.

Contribution

It introduces a kinetic approach to describe fluctuation correlations in an ordered lattice gas, extending beyond diffusion models and accurately capturing small-time behavior.

Findings

Analytical results agree with Monte Carlo simulations.

Defect displacements drive particle number fluctuations.

Kinetic equations effectively describe short-time correlations.

Abstract

We obtain the dynamic correlation function of two-dimensional lattice gas with nearest-neighbor repulsion in ordered c(2$\times$2) phase (antiferromagnetic ordering) under the condition of low concentration of structural defects. It is shown that displacements of defects of the ordered state are responsible for the particle number fluctuations in the probe area. The corresponding set of kinetic equations is derived and solved in linear approximation on the defect concentration. Three types of strongly correlated complex jumps are considered and their contribution to fluctuations is analysed. These are jumps of excess particles, vacancies and flip-flop jumps. The kinetic approach is more general than the one based on diffusion-like equations used in our previous papers. Thus, it becomes possible to adequately describe correlations of fluctuations at small times, where our previous theory fails to give correct results. Our new analytical results for fluctuations of particle number in the probe area agree well with those obtained by Monte Carlo simulations.