Critical exponents of the pair contact process with diffusion

Abstract

We study the pair contact process with diffusion (PCPD) using Monte Carlo simulations, and concentrate on the decay of the particle density $ρ$ with time, near its critical point, which is assumed to follow $ρ(t) \approx ct^{-δ} +c_2t^{-δ_2}+...$. This model is known for its slow convergence to the asymptotic critical behavior; we therefore pay particular attention to finite-time corrections. We find that at the critical point, the ratio of $ρ$ and the pair density $ρ_p$ converges to a constant, indicating that both densities decay with the same powerlaw. We show that under the assumption $δ_2 \approx 2 δ$, two of the critical exponents of the PCPD model are $δ= 0.165(10)$ and $β= 0.31(4)$, consistent with those of the directed percolation (DP) model.