# Kinetics of Phase Separation in the Driven Lattice Gas: Self-Similar Pattern Growth under Anisotropic Nonequilibrium Conditions Source: [Kinetics of Phase Separation in the Driven Lattice Gas: Self-Similar Pattern Growth under Anisotropic Nonequilibrium Conditions]() Collection index: [llms.txt]() Data updated: 2025-10-24T11:06:39.502Z Authors: Pablo I. Hurtado, J. Marro, Pedro L. Garrido, E.V. Albano Published: 2003-02-12T18:26:49.000Z ## 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()