Critical behavior of a two-species reaction-diffusion problem

We present a Monte Carlo study in dimension d=1 of the two-species reaction-diffusion process A+B-->2B and B-->A. Below a critical value rho(c) of 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(st)(B) is the order parameter. This system is related to directed percolation but in a different universality class identified by Kree et al. [Phys. Rev. A 39, 2214 (1989)]. We present an algorithm that enables us to simulate simultaneously the full range of densities rho between zero and some maximum density. From finite-size scaling we obtain the steady state exponents beta=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 exponent takes the value straight theta(')=0.30(2), in agreement with the theoretical relation straight theta(')=-eta/2 due to Van Wijland et al. [Physica A 251, 179 (1998)].