Fluctuation-induced first order transition in a nonequilibrium steady state

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We present the first example of a phase transition in a nonequilibrium steady-state that can be argued analytically to be first order. The system of interest is a two-species reaction-diffusion problem whose control parameter is the total density ρ. Mean-field theory predicts a second-order transition between two stationary states at a critical density ρ=ρc. We develop a phenomenological picture that, instead, below the upper critical dimension dc=4, predicts a first-order transition. This picture is confirmed by hysteresis found in numerical simulations, and by the study of a renormalization-group improved equation of state. The latter approach is inspired by the Weinberg-Coleman mechanism in QED.