  The parity conserving branching-annihilating random walk (pc-BARW) model is a
reaction-diffusion system on a lattice where particles can branch into $m$
offsprings with even $m$ and hop to neighboring sites. If two or more particles
land on the same site, they immediately annihilate pairwise. In this way the
number of particles is preserved modulo two. It is well known that the pc-BARW
with $m=2$ in 1 spatial dimension has no phase transition (it is always
subcritical), if the hopping is described by a continuous time random walk. In
contrast, the $m=2$ 1-d pc-BARW has a phase transition when formulated in
discrete time, but we show that the continuous time limit is non-trivial: When
the time step $\delta t\to 0$, the branching and hopping probabilities at the
critical point scale with different powers of $\delta t$. These powers are
different for different microscopic realizations. Although this phenomenon is
not observed in some other reaction-diffusion systems like, e.g. the contact
process, we argue that it should be generic and not restricted to the 1-d
pc-BARW model.
