Exact results for a chemical reaction model

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Abstract
We study a model of Fichthorn, Gulari, and Ziff for the reaction A+B→0. Their numerical studies showed a transition to a bistable state. We solve the model exactly. Our solution is similar in form to that in diffusion-limited reactions and segregation occurs for low-dimensional substrates. The transition to bistability and saturation for finite-size systems at low desorption probability depend on dimension. The power spectrum of the saturation and the reaction rate are different: The first is universal and the other is sensitive to the geometry of the substrate.