Critical behavior of a two-species reaction-diffusion problem

We present a Monte Carlo study in dimension d = 1 of the two-species reacti on-diffusion process A + B -->2B and B-->A. Below a critical value rho(c) o f the conserved total density rho the system falls into an absorbing state without B particles. Above rho(c) the steady state B particle density rho(B )(st) is the order parameter. This system is related to directed percolatio n but in a different universality class identified by Kree et al. [Phys. Re v. A 39, 2214 (1989)]. We present an algorithm that enables us to simulate simultaneously the full range of densities rho between zero and some maximu m density. From finite-size scaling we obtain the steady state exponents be ta = 0.435(10), nu = 2.21(5), and eta = - 0.606(4) for the order parameter the correlation length, and the critical correlation function, respectively . Independent simulation indicates that the critical initial increase expon ent takes the value theta' = 0.30(2), in agreement with the theoretical rel ation theta' = - eta/2 due to Van Wijland et al.