Phase transitions in an exactly soluble one-dimensional exclusion process

TL;DR

This paper provides an exact solution for a one-dimensional exclusion process with particle injection and removal, revealing a phase diagram that differs from mean field predictions, thus advancing understanding of phase transitions in such models.

Contribution

The authors extend the exact solution of a one-dimensional exclusion process to general injection and removal rates, revealing new phase transition behaviors.

Findings

Exact phase diagram differs from mean field predictions

Solution applicable to general injection and removal rates

Identifies distinct phase transition regimes

Abstract

We consider an exclusion process, with particles injected with rate $\alpha$ at the origin and removed with rate $\beta$ at the right boundary of a one-dimensional chain of sites. The particles are allowed to hop onto unoccupied sites, to the right only. For the special case of $\alpha=\beta=1$ the model was solved previously by Derrida et al. Here we extend the solution to general $\alpha,\beta$. The phase diagram obtained from our exact solution differs from the one predicted by the mean field approximation.