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Algebraic Spatial Correlations and Non-Gibbsian Equilibrium States

Non-Gibbsian stationary states occur in dissipative non-equilibrium systems. They are closely connected with the lack of detailed balance and the absence of a fluctuation-dissipation theorem. These states exhibit spatial correlations that are long ranged under generic conditions, even in systems with short range interactions, provided the system has slow modes and some degree of spatial anisotropy. In this paper we present a theory for static pair correlations in lattice gas automata violating detailed balance, and we show that the spatially uniform non-Gibbsian equilibrium state exhibits long range correlations, even in the absence of an external driving field.