Dynamical mean-field approximations for a diffusive pair contact process

Dynamical mean-field approximations are performed to study the phase transition of a pair contact process with diffusion in different spatial dimensions. The level of approximation is extended up to 18-site clusters for the one-dimensional model. The application of coherent anomaly method shows that the critical $\beta$ exponent does not depend on the strength of diffusion rate. The extension of the mean-field approximation to higher dimensions also suggests that the critical behavior may be described by a unique set of exponents.