Analysis of a pattern-forming lattice-gas automaton: Mean-field theory and beyond

Publisher Website
Google Scholar
Abstract
An analysis is presented of a two-dimensional lattice model of random walkers that interact through a nearest neighbor attraction. The model exhibits a dynamical phase transition to a spatially unstable state, leading to pattern formation and domain coarsening. A mean-field theory is formulated. It is applied to predict the critical temperature and to explain observed anisotropic behavior. The occurrence of a striped phase in the presence of an external driving field is clarified, and a linear response theorem relating the induced particle flux to the variance of equilibrium fluctuations is derived. To account for deviations from mean-field theory, an Enskog-Boltzmann equation is derived that accounts for the effect of static pair correlations existing in equilibrium due to the lack of detailed balance. For temperatures above the critical temperature we obtain corrections to mean-field theory for the diffusion coefficient. Below the critical temperature the theory is used to explain the initial stages of phase separation. © 1996 The American Physical Society.