go to zero, which is clearly different from the $w=0$ case. ](ParkFig6.eps){width="45.00000%"}

Since the models at $w=0$ and at $w\neq 0$ belong to the same DP universality class, it is natural to ask what is the origin of such a nontrivial singularity near the PCP critical point. The inset of Fig. \[Fig:pair\] gives a hint to this question, which shows that the scaling function ${\cal H}$ (the amplitude of the critical decay) does not approach the PCP value as $w$ goes to zero, i.e., it is not continuous at $w=0$. The discontinuity in this amplitude must originate again from the discontinuity in the auxiliary field (particle) density. One can see it directly from the behavior of the particle density ($\rho$). Unlike the pair density, $\rho$ can not be described by the scaling function . Consider again the case at $\Delta = 0$ and nonzero $w$. For any finite value of $w$ in the thermodynamic limit, $\rho(t)$ approaches to zero as $t\rightarrow \infty$; see Fig. \[Fig:single\]. On the other hand, the model at $\Delta =
w=0$ (the critical PCP), has a nonzero density of $\rho(t)$ as $t\rightarrow \infty$. In other words, the $w\rightarrow 0$ limiting process is different from the $w=0$ 