A renormalization group study of a class of reaction-diffusion models, with particles input

We study a class of reaction-diffusion models extrapolating continuously between the pure coagulation-diffusion case and the pure annihilation-diffusion one with particles input at a rate J. For dimension d ≤ 2, the dynamics strongly depends on the fluctuations while, for d > 2, the behaviour is mean-field like. The models are mapped onto a field theory whose properties are studied in a renormalization group approach. Simple relations are found between the time-dependent correlation functions of the different models of the class. For the pure coagulation-diffusion model the time-dependent density is found to be of the form c(t,J,D)=(J/D)1/δ F[(J/D)ΔDt], where D is the diffusion constant. The critical exponent δ and Δ are computed to all orders in ε = 2-d, where d is the dimension of the system, while the scaling function F is computed to second order in ε. For the one-dimensional case an exact analytical solution is provided whose predictions are compared with the results of the renormalization group approach for ε = 1