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.
M. Y. Lee and T. Vojta, "Absorbing-State Phase Transitions on Percolating Lattices," Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, American Physical Society (APS), Apr 2009.
The definitive version is available at http://dx.doi.org/10.1103/PhysRevE.79.041112
Max-Planck-Institut für Physik Komplexer Systeme
National Science Foundation (U.S.)
University of Missouri Research Board
Keywords and Phrases
Monte Carlo Methods; Critical Points; Fluctuations; Phase Transformations; Reaction-Diffusion Systems; Geometry; Percolation
Article - Journal
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