Exactly solvable model of monomer-monomer reactions on a two-dimensional random catalytic substrate

We study the equilibrium properties of a monomer-monomer A+B--> reaction on a two-dimensional substrate containing randomly placed catalytic bonds. Interacting A and B species undergo continuous exchanges with particle reservoirs and react as soon as a pair of unlike particles appears on sites connected by a catalytic bond. For annealed disorder in the placement of catalytic bonds the model is mapped onto a general spin S=1 model and solved exactly for the pressure in a particular case. At equal activities of the two species a second order phase transition is revealed.