Microscopic Theory for Long Range Spatial Correlations in Lattice Gas Automata

Details Microscopic Theory for Long Range Spatial Correlations in Lattice Gas Automata Microscopic Theory for Long Range Spatial Correlations in Lattice Gas Automata

1996-03-05

arxiv.org/abs/cond-mat/9603030v2

Phys. Rev. E 53, 5837-5851 (1996)

Physics

Condensed Matter

31 pages, 2 figures, final version as published

Scientific paper

10.1103/PhysRevE.53.5837

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.

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