Phase transition in an exactly solvable reaction-diffusion process

Abstract

We study a non-conserved one-dimensional stochastic process which involves two species of particles $A$ and $B$. The particles diffuse asymmetrically and react in pairs as $A\varnothing \leftrightarrow AA\leftrightarrow BA\leftrightarrow A\varnothing$ and $B\varnothing \leftrightarrow BB\leftrightarrow AB\leftrightarrow B\varnothing$. We show that the stationary state of the model can be calculated exactly by using matrix product techniques. The model exhibits a phase transition at a particular point in the phase diagram which can be related to a condensation transition in a particular zero-range process. We determine the corresponding critical exponents and provide a heuristic explanation for the unusually strong corrections to scaling seen in the vicinity of the critical point.

10 pages, 8 color figures

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Cited by in corpus (6)

• Theoretical approaches to the steady-state statistical physics of interacting dissipative units
• Statistics of sums of correlated variables described by a matrix product ansatz
• General limit distributions for sums of random variables with a matrix product representation
• Phase Separation Transition in a Nonconserved Two Species Model
• Multi species asymmetric simple exclusion process with impurity activated flips
• A new family of exactly solvable disordered reaction-diffusion systems