Microscopic theory for long-range spatial correlations in lattice gas automata

Abstract

Lattice gas automata with collision rules that violate the conditions of semidetailed 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/r2, and an isotropic fluid-type model with momentum correlations decaying as 1/r2. The pair correlation function for an interacting random walker model with interactions satisfying all symmetries of the square lattice is shown to have 1/r4 density correlations. Theoretical predictions for the amplitude of the algebraic tails are compared with the results of computer simulations.