Critical properties of the reaction-diffusion model2A→3A,2A→0

The steady-state phase diagram of the one-dimensional reaction-diffusion model $2\overrightarrow{A}3A,$ $2\overrightarrow{A}0$ is studied through the non-Hermitian density matrix renormalization group. In the absence of single-particle diffusion the model reduces to the pair-contact process, which has a phase transition in the universality class of directed percolation (DP) and an infinite number of absorbing steady states. When single-particle diffusion is added, the number of absorbing steady states is reduced to 2 and the model no longer shows DP critical behavior. The exponents $\theta ={\nu }_{\Vert }/{\nu }_{\perp }$ and $\beta /{\nu }_{\perp }$ are calculated numerically. The value of $\beta /{\nu }_{\perp }$ is close to the value of the parity conserving universality class, in spite of the absence of local conservation laws.