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arXiv · 1305.6711

Phase transition in an exactly solvable reaction-diffusion process

Somayeh Zeraati·Farhad H. Jafarpour·Haye Hinrichsen
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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 $A\emptyset\leftrightarrow AA\leftrightarrow BA \leftrightarrow A\emptyset$ and $B\emptyset \leftrightarrow BB \leftrightarrow AB \leftrightarrow B\emptyset$. 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.

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Somayeh Zeraati, Farhad H. Jafarpour, Haye Hinrichsen. 2013-05-29. Phase transition in an exactly solvable reaction-diffusion process. https://doi.org/10.1103/physreve.87.062120

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