Lattice gas automata with self-organization

Abstract

Abstract Self-organization or dynamic phase transitions occur in computer simulations of a lattice gas model with strictly local collision dynamics, conserving number of particles, momentum and lattice symmetries. The microscopic collision processes are biased, i.e. they have asymmetric transition rates. In this model, a spatially uniform initial state is unstable. At the onset of instability long wavelength sound modes drive the system into a state with very long range order, with dynamics similar to spinodal decomposition. The structure factor S(k, t) and the selected wavelength for maximal growth, λmax∼tα, are measured as a function of time. The state with long range order is highly organized into moving stable spatial patterns of triangles or parallel strips of macroscopic size (with two or one broken symmetry, respectively). The entropy suddenly drops at self-organization. Both the onset of metastability and the detailed structure of the final patterns are explained by mean field theory.