Simplest nonequilibrium phase transition into an absorbing state

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.

9 pages, 7 figures, minor changes

References in corpus (4)

• Directed percolation criticality in turbulent liquid crystals
• A dynamically extending exclusion process
• Boundary-induced nonequilibrium phase transition into an absorbing state
• Nonequilibrium phase transition in a spreading process on a timeline