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We present an \textit{exactly solvable} model of a monomer-monomer $A + B \to\emptyset$ reaction on a 2D inhomogeneous, catalytic substrate and study theequilibrium properties of the two-species adsorbate. The substrate containsrandomly placed catalytic bonds of mean density $q$ which connect neighboringadsorption sites. The interacting $A$ and $B$ (monomer) species undergocontinuous exchanges with corresponding adjacent gaseous reservoirs. A reaction$A + B \to \emptyset$ takes place instantaneously if $A$ and $B$ particlesoccupy adsorption sites connected by a catalytic bond. We find that for thecase of \textit{annealed} disorder in the placement of the catalytic bonds thereaction model under study can be mapped onto the general spin $S = 1$ (GS1)model. Here we concentrate on a particular case in which the model reduces toan exactly solvable Blume-Emery-Griffiths (BEG) model (T. Horiguchi, Phys.Lett. A {\bf 113}, 425 (1986); F.Y. Wu, Phys. Lett. A, {\bf 116}, 245 (1986))and derive an exact expression for the disorder-averaged equilibrium pressureof the two-species adsorbate. We show that at equal partial vapor pressures ofthe $A$ and $B$ species this system exhibits a second-order phase transitionwhich reflects a spontaneous symmetry breaking with large fluctuations andprogressive coverage of the entire substrate by either one of the species.Comment: 4 pages, 2 figures, submitted to Phys. Rev. Let

Exactly Solvable Model of Monomer-Monomer Reactions on a Two-Dimensional Random Catalytic Substrate