$1/\rho_0$. If $0< D\rho_0^2 \ll
\tau^{-1}$ with the diffusion constant $D$, the “defect dynamics” will continue again indefinitely for small $D$. So the phase boundary in the $D-p$ plane should have a discontinuity at $D=0$.

                  $w$ $p_c(w)$
  ------------------- ------------------
    $0              $ $0.077~0905 (5)$
    $10^{-5}        $ $0.077~002  (3)$
    $5\times 10^{-5}$ $0.076~885  (3)$
    $10^{-4}        $ $0.076~784  (4)$
    $2\times 10^{-4}$ $0.076~642  (2)$
    $3\times 10^{-4}$ $0.076~530  (5)$
    $4\times 10^{-4}$ $0.076~432  (2)$
    $5\times 10^{-4}$ $0.076~345  (2)$
    $6\times 10^{-4}$ $0.076~264  (1)$
    $10^{-3}        $ $0.075~988  (4)$

  : \[Table:PCP\_pc\] Critical points of the model with dynamics of Eq.  for some values of $w$’s at $q=0$. The numbers in the parentheses indicate the error of the last digits.

Let us turn to the crossover model with $q=0$, which should represent a typical inhibitory route. Table \[Table:PCP\_pc\] summarizes the critical points of the model for some $w$’s at $q=0$ and the corresponding phase boundary is plotted in Fig. \[Fig:PCPphase\]. Unlike the previous case, the reactive phase shrinks continuously with the rate of additional single-particle annihilation process and the phase boundary is continuous. The usual analysis method can be applied to this case [@DL9]. If we define $\Delta = (p_0 - p)/p_0$ and $\Delta_c(w)
= (p_0 - p_c(w))/p_0$, the phase boundary 