Absorbing-state phase transitions on percolating lattices

Abstract

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.

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

References in corpus (29)

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• Percolation quantum phase transitions in diluted magnets
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• Low-energy dynamics of the two-dimensional S=1/2 Heisenberg antiferromagnet on percolating clusters
• The generalized contact process with n absorbing states
• Multicritical behavior of the diluted contact process

Cited by in corpus (8)

• Griffiths phases on complex networks
• Rare region effects in the contact process on networks
• Monte-Carlo simulations of the clean and disordered contact process in three dimensions
• Infinite-noise criticality: Nonequilibrium phase transitions in fluctuating environments
• Contact process on generalized Fibonacci chains: infinite-modulation criticality and double-log periodic oscillations
• Contact process with temporal disorder
• Phase transitions of the generalized contact process with two absorbing states
• Contact process with simultaneous spatial and temporal disorder