Abstract
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=ρ c. We develop a phenomenological picture that instead predicts a first-order transition below the upper critical dimension d c=4. 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 Coleman–Weinberg mechanism in QED.
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