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Driven far away from equilibrium by both uniform and random external fields, a system of diffusing particles with short-range attractive forces displays many singular thermodynamic properties. Surprisingly, measuring pair correlations in lattice-gas models with saturation drives, we find little difference between the uniform and random cases, even though the underlying symmetries are quite distinct. Motivated by this puzzle, we study three-point correlations using both field-theoretic anddoi:10.1103/physreve.48.800 pmid:9960661 fatcat:ziwmxmcwtzfnvfzhqsuy4r43u4