  We study the equilibrium properties of a model for a binary mixture of
catalytically-reactive monomers adsorbed on a two-dimensional substrate
decorated by randomly placed catalytic bonds. The interacting $A$ and $B$
monomer species undergo continuous exchanges with particle reservoirs and react
($A + B \to \emptyset$) as soon as a pair of unlike particles appears on sites
connected by a catalytic bond.
  For the case of annealed disorder in the placement of the catalytic bonds
this model can be mapped onto a classical spin model with spin values $S =
-1,0,+1$, with effective couplings dependent on the temperature and on the mean
density $q$ of catalytic bonds. This allows us to exploit the mean-field theory
developed for the latter to determine the phase diagram as a function of $q$ in
the (symmetric) case in which the chemical potentials of the particle
reservoirs, as well as the $A-A$ and $B-B$ interactions are equal.

Statistical Mechanics;Materials Science