Binary reactive adsorbate on a random catalytic substrate

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→) 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