Analytical solution of an irreversible surface reaction model

Abstract

In this work, we consider a simple model of reaction-limited annihilation A + B → 0 with a random source and desorption in the spirit of the reaction model proposed by Fitchthorn, Ziff, and Gulari, and we solve it exactly using a spin model. We show that the situation is similar to a diffusion-limited kinetic situation (though diffusion was a priori absent from the model). We find the occurrence of a large-scale organization phenomenon at low dimension called segregation, and for a finite size system, a transition to a saturated state at low desorption probability. We show how this transition is affected by the dimensionality of the substrate. We also show how the fluctuation spectrum of two quantities such as the saturation and the reaction rate can be drastically different, the first being universal and the other sensitive to the geometry of the substrate.