1202.4930 (R. D. Schram et al.)

Critical exponents of the pair contact process with diffusion    [PDF]

R. D. Schram, G. T. Barkema

We study the pair contact process with diffusion (PCPD) using Monte Carlo
simulations, and concentrate on the decay of the particle density $\rho$ with
time, near its critical point, which is assumed to follow $\rho(t) \approx
ct^{-\delta} +c_2t^{-\delta_2}+...$. 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 $\rho$ and the pair density $\rho_p$ converges to a constant,
indicating that both densities decay with the same powerlaw. We show that under
the assumption $\delta_2 \approx 2 \delta$, two of the critical exponents of
the PCPD model are $\delta = 0.165(10)$ and $\beta = 0.31(4)$, consistent with
those of the directed percolation (DP) model.

View original: http://arxiv.org/abs/1202.4930