Absorbing phase transitions on random Voronoi triangulations

Nonequilbrium phase transitions from an active (fluctuating) to an inactive (absorbing) phase in spatially extended systems is a topic of current great interest. The so-called absorbing state phase transitions (APT) arise in a wide variety of problems, for example, heterogeneous catalysis, interface growth, population dynamics and epidemiology. Recent experimental realizations in turbulent liquid crystals, driven suspensions and superconducting vortices increased the interest in this kind of transitions. Of particular interest is how spatially quenched disorder affects the critical behavior of APT. In real systems, quenched disorder appears in the form of impurities and defects. On a regular lattice, quenched disorder can be added in the forms of random deletion of sites or bonds or of random spatial variation of the control parameter. In all the cases above, one finds a change in the critical behavior of the model, with strong Griffiths singularities.

An important question is what happens when the disorder is configurational, {\em i.e.}, when the underlying graph is not periodic, as observed in a deterministic aperiodic structure, or in a graph with a random connectivity such as the Voronoi triangulation. The Voronoi lattice represents a natural way of introducing quenched coordination disorder in a lattice model, and also plays an important role in the description of idealized statistical geometries such as planar cellular structures, soap throats, etc.

In this work, we study first-order and second-order absorbing-state phase transitions on the Voronoi-Delaunay lattice. Our extensive simulations confirm recent findings of Barghatti and Vojta [1] on the effects of random topological (connectivity) disorder. We observe that such kind of disorder is irrelevant for the critical behavior for models belonging to the directed percolation and manna universality class. Using the ZGB model as example, we show that the coordination disorder is not capable of changing the nature of the transition, as occurs when uncorrelated random defects are present in the substrate.

[1] H. Barghathi and T. Vojta, Phys. Rev. Lett. {\bf 113}, 120602 (2014)

\hspace{10cm}Supporting Agencies: FAPEMIG and CNPq.