Phase transition in an exactly solvable reaction-diffusion process

TL;DR

This paper analyzes an exactly solvable one-dimensional reaction-diffusion model with two particle species, revealing a phase transition linked to a condensation phenomenon, and calculates critical exponents using matrix product methods.

Contribution

It introduces an exactly solvable reaction-diffusion process with a phase transition, providing explicit calculations of stationary states and critical behavior.

Findings

Identifies a phase transition in the model

Calculates critical exponents for the transition

Links the transition to a condensation in a zero-range 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 $A\emptyset\leftrightarrow AA\leftrightarrow BA \leftrightarrow A\emptyset$ 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.