Simplest nonequilibrium phase transition into an absorbing state

TL;DR

This paper investigates simple one-dimensional particle models with boundary-induced absorbing state phase transitions, revealing a universality class with non-trivial critical exponents and discussing their relation to non-Markovian processes.

Contribution

It provides a detailed analysis of various boundary-driven particle models, identifying their critical behavior and universality class, and introduces a connection to non-Markovian dynamics.

Findings

Most models exhibit non-trivial critical exponents

One exactly solvable bosonic variant shows a discontinuous transition

Models belong to a distinct universality class

Abstract

We study in further detail particle models displaying a boundary-induced absorbing state phase transition [Phys. Rev. E. {\bf 65}, 046104 (2002) and Phys. Rev. Lett. {\bf 100}, 165701 (2008)] . These are one-dimensional systems consisting of a single site (the boundary) where creation and annihilation of particles occur and a bulk where particles move diffusively. We study different versions of these models, and confirm that, except for one exactly solvable bosonic variant exhibiting a discontinuous transition and trivial exponents, all the others display non-trivial behavior, with critical exponents differing from their mean-field values, representing a universality class. Finally, the relation of these systems with a $(0+1)$-dimensional non-Markovian process is discussed.