Microscopic Theory for Long Range Spatial Correlations in Lattice Gas Automata
Abstract
Lattice gas automata with collision rules that violate the conditions of semi-detailed-balance exhibit algebraic decay of equal time spatial correlations between fluctuations of conserved densities. This is shown on the basis of a systematic microscopic theory. Analytical expressions for the dominant long range behavior of correlation functions are derived using kinetic theory. We discuss a model of interacting random walkers with x-y anisotropy whose pair correlation function decays as 1/r^2, and an isotropic fluid-type model with momentum correlations decaying as 1/r^2. The pair correlation function for an interacting random walker model with interactions satisfying all symmetries of the square lattice is shown to have 1/r^4 density correlations. Theoretical predictions for the amplitude of the algebraic tails are compared with the results of computer simulations.
Cite
@article{arxiv.cond-mat/9603030,
title = {Microscopic Theory for Long Range Spatial Correlations in Lattice Gas Automata},
author = {H. J. Bussemaker and M. H. Ernst},
journal= {arXiv preprint arXiv:cond-mat/9603030},
year = {2009}
}
Comments
31 pages, 2 figures, final version as published