Absorbing-state phase transitions on percolating lattices

Details Absorbing-state phase transitions on percolating lattices Absorbing-state phase transitions on percolating lattices

2009-01-14

arxiv.org/abs/0901.1995v3

Phys. Rev. E 79, 041112 (2009)

Physics

Condensed Matter

Statistical Mechanics

11 pages, 10 eps figures included, final version as published

Scientific paper

10.1103/PhysRevE.79.041112

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 new 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.

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