Fluctuation-induced first-order transition in a nonequilibrium steady state

We present the first example of a phase transition in a nonequilibrium stea dy state that ran be argued analytically to be first order. The system of i nterest is a two-species reaction-diffusion problem whose control parameter is the total density rho. Mean-field theory predicts a second-order transi tion between two stationary states at a critical density rho=rho(c). We dev elop a phenomenological picture that instead predicts a first-order transit ion below the upper critical dimension d(c)=4. This picture is confirmed by hysteresis found in numerical simulations, and by the study of a renormali zation-group improved equation of state. The latter approach is inspired by the Coleman-Weinberg mechanism in QED.