Kinetics of Phase Separation in the Driven Lattice Gas: Self-Similar Pattern Growth under Anisotropic Nonequilibrium Conditions

TL;DR

This paper investigates the pattern formation kinetics in the driven lattice gas under anisotropic nonequilibrium conditions, revealing self-similar growth characterized by a $t^{1/3}$ scaling law driven by particle processes.

Contribution

It provides a theoretical and simulation-based analysis of pattern growth in the driven lattice gas, highlighting the role of single-particle processes and anisotropy in self-similar pattern evolution.

Findings

Pattern growth follows a $t^{1/3}$ law in macroscopic systems.

Surface evaporation/condensation dominates early, then bulk hole diffusion prevails.

Anisotropy critically influences the emergent pattern behavior.

Abstract

The driven lattice gas (DLG) evolving at low temperature helps understanding the kinetics of pattern formation in unstable mixtures under anisotropic conditions. We here develop a simple theoretical description of kinetics in Monte Carlo simulations of the DLG. A Langevin continuum analog is also studied which is shown to exhibit the same behavior. We demonstrate that pattern growth is mainly a consequence of single-particle processes and that, after a short transient time, in which a surface evaporation/condensation mechanism is important, hole diffusion in the bulk becomes dominant. Consequently, there is a unique relevant length that behaves $l(t) \sim t^{1/3}$ for macroscopic systems except at some very early (perhaps unobservable) time. This implies sort of self-similarity, namely, the spatial pattern looks alike, but for a (non-trivial) change of scale at different times. We also characterize the structure factor, in which we identify Guinier and Porod regions, and its scaling form with both time and size. The underlying anisotropy turns out to be essential in determining the macroscopically-emergent peculiar behavior.