  We investigate phase coexistence in a weakly stochastic reaction-diffusion
system without assuming a continuum description. Concretely, for $(2N+1)$
diffusion-coupled vessels in which a chemical reaction exhibiting bistability
occurs, we derive a condition for the phase coexistence in the limit $N \to
\infty$. We then find that the phase coexistence condition depends on the rate
of hopping between neighboring vessels. The conditions in the high- and
low-hopping-rate limits are expressed in terms of two different potentials
which are determined from the chemical reaction model in a single vessel.
