Phase transition of the one-dimensional coagulation-production process

Recently an exact solution has been found by M. Henkel and H. Hinrichsen [J. Phys. A 34, 1561 (2001)] for the one-dimensional coagulation-production process: $2\overrightarrow{A}A,\hspace{0.5em}\hspace{0.5em}A\mathrm{Ø}\overrightarrow{A}3A$ with equal diffusion and coagulation rates. This model evolves into the inactive phase independently of the production rate with $t^{-1/2}$ density decay law. This paper shows that cluster mean-field approximations and Monte Carlo simulations predict a continuous phase transition for higher diffusion/coagulation rates as considered by the exact solution. Numerical evidence is given that the phase transition universality agrees with that of the annihilation-fission model with low diffusions.