of the DP ($\simeq 1.733$), the accuracy of the critical points in Table \[Table:DI\_pc\] is worse than that for the DP cases. From these data, one can estimate the crossover exponent $1/\phi_\text{DI}$ as $0.34(4)$ which should be compared with $1/\nu_\|$ of the DI class ($\simeq 0.31$). Hence we conclude that our argument for $\phi=\nu_\|$ also applies to the crossover from the IM-type DI to the DI models.

\[Sec:dptodp\]Diffusion effect
==============================

This section studies how the crossover scaling is affected if particles are allowed to hop in models considered in Sec. \[Sec:dpima\]. With single-particle diffusion, the PCP becomes the PCPD where the particle (auxiliary field) density as well as the pair density vanishes at criticality even without any single-particle reaction process. The crossover from the PCPD to the DP caused by including single-particle reactions has been studied previously by the present authors [@PP06] where the value of the crossover exponent is reported as $1/\phi = 0.58(3)$. This value is quite close to that obtained for the crossover from the DP${}_\textrm{IM}$ to the DP in Sec. \[Sec:dpima\]. This similarity may mislead one to jump to the wrong conclusion that the critical nature of the PCP and the PCPD is equivalent. However, one 