We study nonequilibrium phase transitions of reaction-diffusion systems defined on randomly diluted lattices, focusing on the transition across the lattice percolation threshold. To develop a theory for this transition, we combine classical percolation theory with the properties of the supercritical nonequilibrium system on a finite-size cluster. In the case of the contact process, the interplay between geometric criticality due to percolation and dynamical fluctuations of the nonequilibrium system leads to a different universality class. The critical point is characterized by ultraslow activated dynamical scaling and accompanied by strong Griffiths singularities. To confirm the universality of this exotic scaling scenario we also study the generalized contact process with several (symmetric) absorbing states and we support our theory by extensive Monte Carlo simulations.




Max-Planck-Institut für Physik Komplexer Systeme
National Science Foundation (U.S.)
Research Corporation
University of Missouri Research Board

Keywords and Phrases

Monte Carlo Methods; Critical Points; Fluctuations; Phase Transformations; Reaction-Diffusion Systems; Geometry; Percolation

Document Type

Article - Journal

Document Version

Final Version

File Type





© 2009 American Physical Society (APS), All rights reserved.

Publication Date

01 Apr 2009

Included in

Physics Commons