  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.
