Continuous and discontinuous absorbing-state phase transitions on Voronoi-Delaunay random lattices

TL;DR

This study investigates how quenched topological disorder in Voronoi-Delaunay lattices affects absorbing-state phase transitions, finding that such disorder does not alter the nature of the transitions in several models.

Contribution

It demonstrates that quenched topological disorder in Voronoi-Delaunay lattices is irrelevant for the critical behavior of certain nonequilibrium phase transitions, including discontinuous and directed percolation models.

Findings

Disorder does not change the discontinuous transition in the ZGB model.

Disorder is irrelevant for directed percolation and Manna universality classes.

Supports the idea that topological disorder can be irrelevant in some nonequilibrium systems.

Abstract

We study absorbing-state phase transitions in two-dimensional Voronoi-Delaunay (VD) random lattices with quenched coordination disorder. Quenched randomness usually changes the criticality and destroys discontinuous transitions in low-dimensional nonequilibrium systems. We performed extensive simulations of the Ziff-Gulari-Barshad (ZGB) model, and verified that the VD disorder does not change the nature of its discontinuous transition. Our results corroborate recent findings of Barghatti and Vojta [Phys. Rev. Lett. {\bf 113}, 120602 (2014)] stating the irrelevance of topological disorder in a class of random lattices that includes VD and raise the interesting possibility that disorder in nonequilibrium APT may, under certain conditions, be irrelevant for the phase coexistence. We also verify that the VD disorder is irrelevant for the critical behavior of models belonging to the directed percolation and Manna universality classes.