Abstract
In this paper we discuss the existence of generic long-range correlations in spatially homogeneous and stable equilibrium states of closed lattice gas automata whose stochastic collision rules violate the symmetry conditions of detailed balance and in addition satisfy local conservation laws. Such correlations occur even though the collision rules are strictly local and invariant under all symmetries of the lattice. First a phenomenological (Langevin equation) approach is discussed. Next we present a theoretical analysis on the basis of an approximate microscopic (ring kinetic) theory. This theory is used to calculate the amplitude ofr −α tails in the spatial correlations, and the result is compared with computer simulations.
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Ernst, M.H., Bussemaker, H.J. Algebraic spatial correlations in lattice gas automata violating detailed balance. J Stat Phys 81, 515–536 (1995). https://doi.org/10.1007/BF02179991
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DOI: https://doi.org/10.1007/BF02179991